Journal of Combinatorial Optimization, ISSN 1382-6905, 5/2017, Volume 33, Issue 4, pp. 1421 - 1442

An L(2, 1)-coloring (or labeling) of a graph G is a mapping $$f:V(G) \rightarrow \mathbb {Z}^{+}\bigcup \{0\}$$ f : V ( G ) → Z + ⋃ { 0 } such that $$|f(u)-f(v)|\ge 2$$ | f ( u ) - f ( v ) | ≥ 2 for all edges uv of G...

No-hole coloring | Mathematics | Theory of Computation | Span of a graph | Optimization | L (2, 1)-coloring | Convex and Discrete Geometry | Irreducible coloring | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Subdivision graph | 05C15 | L(2, 1)-coloring | MATHEMATICS, APPLIED | DISTANCE-2 | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | L(2,1)-LABELINGS | LABELINGS | L(2,1)-coloring

No-hole coloring | Mathematics | Theory of Computation | Span of a graph | Optimization | L (2, 1)-coloring | Convex and Discrete Geometry | Irreducible coloring | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Subdivision graph | 05C15 | L(2, 1)-coloring | MATHEMATICS, APPLIED | DISTANCE-2 | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | L(2,1)-LABELINGS | LABELINGS | L(2,1)-coloring

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2018, Volume 38, Issue 2, pp. 525 - 552

... (2, 1)-colorings of . For an (2, 1)-coloring of a graph with span , an integer is a in...

subdivision graph | no-hole coloring | edge-multiplicity-paths-replacement graph | irreducible coloring | (2,1)-coloring | 05C15 | MATHEMATICS | DISTANCE-2 | L(2,1)-LABELINGS | L(2,1)-coloring

subdivision graph | no-hole coloring | edge-multiplicity-paths-replacement graph | irreducible coloring | (2,1)-coloring | 05C15 | MATHEMATICS | DISTANCE-2 | L(2,1)-LABELINGS | L(2,1)-coloring

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 07/2003, Volume 16, Issue 4, pp. 651 - 662

.... This implies bounds for the chromatic number as well, since the inductiveness naturally relates to a greedy algorithm for vertex-coloring the given graph...

Radio coloring | Distance-2 coloring | MATHEMATICS, APPLIED | ROOTS | radio coloring | APPROXIMATION ALGORITHMS | distance-2 coloring

Radio coloring | Distance-2 coloring | MATHEMATICS, APPLIED | ROOTS | radio coloring | APPROXIMATION ALGORITHMS | distance-2 coloring

Journal Article

Networks, ISSN 0028-3045, 03/2009, Volume 53, Issue 2, pp. 206 - 211

.... This is modeled as an L(2, 1)‐coloring of a graph which is no‐hole and irreducible in the sense that no color can be replaced with a smaller one...

tree | L(2, 1)‐coloring | channel assignment problem | irreducible coloring | Irreducible coloring | Tree | Channel assignment problem | L(2, 1)-coloring | COLORINGS | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | LABELING GRAPHS | DISTANCE-2 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CHANNEL-ASSIGNMENT | CYCLES | L(2,1)-LABELINGS | L(2,1)-coloring | CARTESIAN PRODUCTS

tree | L(2, 1)‐coloring | channel assignment problem | irreducible coloring | Irreducible coloring | Tree | Channel assignment problem | L(2, 1)-coloring | COLORINGS | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | LABELING GRAPHS | DISTANCE-2 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CHANNEL-ASSIGNMENT | CYCLES | L(2,1)-LABELINGS | L(2,1)-coloring | CARTESIAN PRODUCTS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 04/2012, Volume 312, Issue 8, pp. 1400 - 1406

The game coloring number of the square of a graph G, denoted by gcol(G2), was first studied by Esperet and Zhu. The (a,b...

Asymmetric coloring game | Distance-2 coloring | Partial [formula omitted]-tree | Planar graph | Game coloring | Partial k-tree | MATHEMATICS | ASYMMETRIC MARKING GAMES | NUMBER | ACTIVATION STRATEGY | Integers | Coloring | Mathematical analysis | Games | Graphs | Orientation | Order disorder

Asymmetric coloring game | Distance-2 coloring | Partial [formula omitted]-tree | Planar graph | Game coloring | Partial k-tree | MATHEMATICS | ASYMMETRIC MARKING GAMES | NUMBER | ACTIVATION STRATEGY | Integers | Coloring | Mathematical analysis | Games | Graphs | Orientation | Order disorder

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 02/2003, Volume 42, Issue 2, pp. 110 - 124

...REFERENCES 1 G. Agnarsson and M. M. Halldórsson , Coloring Powers of planar graphs . Preprint ( 2000 ). 2 K. Appel and W. Haken , Every planar map is four...

chromatic number | labeling of a graph | planar graph | Chromatic number | Labeling of a graph | Planar graph | MATHEMATICS | DISTANCE-2 | MAP

chromatic number | labeling of a graph | planar graph | Chromatic number | Labeling of a graph | Planar graph | MATHEMATICS | DISTANCE-2 | MAP

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2010, Volume 310, Issue 17, pp. 2327 - 2333

The square G 2 of a graph G is defined on the vertex set of G in such a way that distinct vertices with distance at most 2 in G are joined by an edge. We study...

Cartesian product of cycles | Distance-2 coloring | Square of graphs | Chromatic number | PATH | MATHEMATICS | NUMBER | PLANAR GRAPH | L(2,1)-LABELINGS | L(D | Cartesian | Coloring | Graphs | Ceilings | Mathematical analysis | Edge joints | Computer Science | Discrete Mathematics

Cartesian product of cycles | Distance-2 coloring | Square of graphs | Chromatic number | PATH | MATHEMATICS | NUMBER | PLANAR GRAPH | L(2,1)-LABELINGS | L(D | Cartesian | Coloring | Graphs | Ceilings | Mathematical analysis | Edge joints | Computer Science | Discrete Mathematics

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2010, Volume 32, Issue 4, pp. 2418 - 2446

The distance-2 graph coloring problem aims at partitioning the vertex set of a graph into the fewest sets consisting of vertices pairwise at distance greater than 2 from each...

Hessian computation | Combinatorial scientific computing | Distributed-memory parallel algorithms | Sparsity exploitation | Distance-2 graph coloring | Automatic differentiation | Jacobian computation | MATHEMATICS, APPLIED | distance-2 graph coloring | APPROXIMATION | combinatorial scientific computing | COMPUTERS | sparsity exploitation | NETWORKS | automatic differentiation | SPARSE HESSIAN MATRICES | PLANAR GRAPHS | distributed-memory parallel algorithms | Studies | Cluster analysis | Parallel processing | Distributed processing | Combinatorics | Iterative methods

Hessian computation | Combinatorial scientific computing | Distributed-memory parallel algorithms | Sparsity exploitation | Distance-2 graph coloring | Automatic differentiation | Jacobian computation | MATHEMATICS, APPLIED | distance-2 graph coloring | APPROXIMATION | combinatorial scientific computing | COMPUTERS | sparsity exploitation | NETWORKS | automatic differentiation | SPARSE HESSIAN MATRICES | PLANAR GRAPHS | distributed-memory parallel algorithms | Studies | Cluster analysis | Parallel processing | Distributed processing | Combinatorics | Iterative methods

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2003, Volume 130, Issue 3, pp. 513 - 519

An L(2,1)- coloring of a graph G is a coloring of G's vertices with integers in {0,1,…, k} so that adjacent vertices...

Channel assignment problems | Distance-two colorings | No-hole colorings | COLORINGS | MATHEMATICS, APPLIED | DISTANCE-2 | distance-two colorings | LABELINGS | no-hole colorings | channel assignment problems | GRAPHS

Channel assignment problems | Distance-two colorings | No-hole colorings | COLORINGS | MATHEMATICS, APPLIED | DISTANCE-2 | distance-two colorings | LABELINGS | no-hole colorings | channel assignment problems | GRAPHS

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 10/2014, Volume 554, Issue C, pp. 22 - 39

In an L(2,1)-coloring of a graph, the vertices are colored with colors from an ordered set such that neighboring vertices get colors that have distance at least 2 and vertices at distance 2 in the graph get different colors...

Advice complexity | Randomized algorithms | Online coloring | Frequency assignment | DISTANCE-2 | LABELING GRAPHS | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Algorithms

Advice complexity | Randomized algorithms | Online coloring | Frequency assignment | DISTANCE-2 | LABELING GRAPHS | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Algorithms

Journal Article

IEEE Transactions on Parallel and Distributed Systems, ISSN 1045-9219, 05/2017, Volume 28, Issue 5, pp. 1240 - 1256

Graph coloring-in a generic sense-is used to identify subsets of independent tasks in parallel scientific computing applications...

Context | Tilera manycore architecture | Color | Standards | partial distance-2 coloring | Balanced coloring | Image color analysis | Processor scheduling | distance-1 coloring | parallel graph coloring | Bipartite graph | community detection | graph algorithms | COMPUTER SCIENCE, THEORY & METHODS | HEURISTICS | ENGINEERING, ELECTRICAL & ELECTRONIC | Image coding | Research | Multiprocessing | Methods | Algorithms | Parallel processing | Graph coloring | Computation | Heuristic

Context | Tilera manycore architecture | Color | Standards | partial distance-2 coloring | Balanced coloring | Image color analysis | Processor scheduling | distance-1 coloring | parallel graph coloring | Bipartite graph | community detection | graph algorithms | COMPUTER SCIENCE, THEORY & METHODS | HEURISTICS | ENGINEERING, ELECTRICAL & ELECTRONIC | Image coding | Research | Multiprocessing | Methods | Algorithms | Parallel processing | Graph coloring | Computation | Heuristic

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 04/2017, Volume 221, pp. 106 - 114

The frequency assignment problem is to assign a frequency to each radio transmitter so that transmitters are assigned frequencies with allowed separations....

Coloring square of graphs | Wireless network | Graph coloring | Frequency assignment | Kneser graph | L(2,1)-labeling | MATHEMATICS, APPLIED | CELLULAR RADIO NETWORKS | LABELING GRAPHS | CHROMATIC NUMBER | STRONG PRODUCTS | CHANNEL ASSIGNMENT | DISTANCE-2 | TREES

Coloring square of graphs | Wireless network | Graph coloring | Frequency assignment | Kneser graph | L(2,1)-labeling | MATHEMATICS, APPLIED | CELLULAR RADIO NETWORKS | LABELING GRAPHS | CHROMATIC NUMBER | STRONG PRODUCTS | CHANNEL ASSIGNMENT | DISTANCE-2 | TREES

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2006, Volume 20, Issue 2, pp. 428 - 443

.... G is full-colorable if some such coloring uses all colors in {0, 1,...,lambda(G)} and no others. We prove that all trees except stars are full-colorable...

Channel assignment problems | Distance-two colorings | No-hole colorings | MATHEMATICS, APPLIED | DISTANCE-2 | distance-two colorings | LABELINGS | no-hole colorings | channel assignment problems | GRAPHS

Channel assignment problems | Distance-two colorings | No-hole colorings | MATHEMATICS, APPLIED | DISTANCE-2 | distance-two colorings | LABELINGS | no-hole colorings | channel assignment problems | GRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 04/2015, Volume 338, Issue 4, pp. 615 - 620

Let G be a finite simple graph. For an integer k≥1, a radio k-coloring of G is an assignment f of non-negative integers to the vertices of G satisfying the condition ∣f(u)−f(v)∣≥k+1−d(u,v...

Circulant graph | Path covering number | Radio [formula omitted]-coloring | Hamiltonian path | Radio k-coloring | MATHEMATICS | DISTANCE-2 | NUMBER | DISJOINT PATHS | LABELINGS | GRAPHS

Circulant graph | Path covering number | Radio [formula omitted]-coloring | Hamiltonian path | Radio k-coloring | MATHEMATICS | DISTANCE-2 | NUMBER | DISJOINT PATHS | LABELINGS | GRAPHS

Journal Article

2019 International Conference on Software, Telecommunications and Computer Networks (SoftCOM), 09/2019, pp. 1 - 6

.... In terms of graph theory, solving this issue amounts to solve the distance-2 coloring problem on the network...

Time slot assignment | Synchronous system | Conflict | Collision | Message-passing | Wireless network | Broadcast/receive | Distance-2 graph coloring

Time slot assignment | Synchronous system | Conflict | Collision | Message-passing | Wireless network | Broadcast/receive | Distance-2 graph coloring

Conference Proceeding

Computer Journal, ISSN 0010-4620, 06/2013, Volume 57, Issue 11, pp. 1639 - 1648

In this paper, we propose a self-stabilizing distance-2 edge coloring algorithm for arbitrary graphs...

Distance-2 edge coloring | Strong edge coloring | Self-stabilizing system | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | strong edge coloring | self-stabilizing system | distance-2 edge coloring | COMPUTER SCIENCE, INFORMATION SYSTEMS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | GRAPHS

Distance-2 edge coloring | Strong edge coloring | Self-stabilizing system | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | strong edge coloring | self-stabilizing system | distance-2 edge coloring | COMPUTER SCIENCE, INFORMATION SYSTEMS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | GRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2006, Volume 154, Issue 10, pp. 1522 - 1540

An L ( 2 , 1 ) -labeling of a graph is an assignment of nonnegative integers to its vertices so that adjacent vertices get labels at least two apart and...

Vertex labeling | Product of cycles | [formula omitted]-labeling | Distance two labeling | [formula omitted]-coloring | L ( 2, 1 )-labeling | L ( 2, 1 )-coloring | MATHEMATICS, APPLIED | DISTANCE-2 | 1)-LABELINGS | vertex labeling | product of cycles | L(D | distance two labeling | LABELINGS | L(2,1)-labeling | L(2,1)-coloring | GRAPHS

Vertex labeling | Product of cycles | [formula omitted]-labeling | Distance two labeling | [formula omitted]-coloring | L ( 2, 1 )-labeling | L ( 2, 1 )-coloring | MATHEMATICS, APPLIED | DISTANCE-2 | 1)-LABELINGS | vertex labeling | product of cycles | L(D | distance two labeling | LABELINGS | L(2,1)-labeling | L(2,1)-coloring | GRAPHS

Journal Article

STACS 2000: 17TH ANNUAL SYMPOSIUM ON THEORETICAL ASPECT OF COMPUTER SCIENCE, ISSN 0302-9743, 2000, Volume 1770, pp. 395 - 406

A lambda -coloring of a graph G is an assignment of colors from the set{0,...,lambda} to the vertices of a graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart...

DISTANCE-2 | RADIO NETWORKS | ALGORITHM | COMPUTER SCIENCE, THEORY & METHODS | LABELINGS

DISTANCE-2 | RADIO NETWORKS | ALGORITHM | COMPUTER SCIENCE, THEORY & METHODS | LABELINGS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2003, Volume 272, Issue 1, pp. 37 - 46

... : V×V×N 0→ Z by F( u, v, m)= δ( u, v)+ m− K. A coloring c of G is an F-coloring if F...

Greedy F-chromatic number | Greedy F-coloring | F-coloring | F-chromatic number | MATHEMATICS | DISTANCE-2 | greedy F-coloring | greedy F-chromatic number

Greedy F-chromatic number | Greedy F-coloring | F-coloring | F-chromatic number | MATHEMATICS | DISTANCE-2 | greedy F-coloring | greedy F-chromatic number

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2003, Volume 129, Issue 2, pp. 449 - 460

...-numbers of the Cartesian product of a cycle and a path are computed, where the λ-number of a graph G is the minimum number of colors needed in a (2,1)-coloring of G...

Cartesian product of graphs | Rotagraph | Strong product of graphs | Dynamic algorithm | Independence number | (2,1)-coloring | PATH | CAPACITY | MATHEMATICS, APPLIED | strong product of graphs | LABELINGS | rotagraph | independence number | DISTANCE-2 | CHANNEL | PRODUCTS | CYCLES | dynamic algorithm

Cartesian product of graphs | Rotagraph | Strong product of graphs | Dynamic algorithm | Independence number | (2,1)-coloring | PATH | CAPACITY | MATHEMATICS, APPLIED | strong product of graphs | LABELINGS | rotagraph | independence number | DISTANCE-2 | CHANNEL | PRODUCTS | CYCLES | dynamic algorithm

Journal Article

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