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2010, 4th ed., Graduate texts in mathematics, ISBN 9783642142789, Volume 173., xviii, 436
Book
Journal of the ACM (JACM), ISSN 0004-5411, 11/2005, Volume 52, Issue 6, pp. 866 - 893
Journal Article
Theoretical computer science, ISSN 0304-3975, 2018, Volume 745, pp. 36 - 52
We introduce the family of k-gap-planar graphs for k≥0, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most k of its crossings... 
k-quasiplanar graphs | Complete graphs | Beyond planarity k-gap-planar graphs | k-planar graphs | Density results | Recognition problem | LINEAR-TIME | NUMBER | CROSSINGS | EDGES | COMPUTER SCIENCE, THEORY & METHODS | 1-PLANARITY
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 217, pp. 304 - 317
...; we call any such graph an a-graph. We state an a-graph coloring problem equivalent to the 4-color problem and then derive a coloring condition that a minimal a-graph counterexample must satisfy, expressing it in terms of equivalence... 
Minimal counterexample | Equivalence class | Birkhoff diamond | Kempe exchange | 4-color problem | MATHEMATICS, APPLIED | EVERY PLANAR MAP
Journal Article
Journal of mechanical design (1990), ISSN 1050-0472, 01/2018, Volume 140, Issue 1
.... The graph theory has been proved to be an effective tool to synthesize and analyze PGTs. This paper aims to propose a new graph model, which has some merits relative to the existing ones, to represent the structure of PGTs... 
displacement graph | ENUMERATION | ENGINEERING, MECHANICAL | structure synthesis | rotation graph | METHODOLOGY | PLANAR KINEMATIC CHAINS | planetary gear train | STRUCTURAL SYNTHESIS | TOPOLOGICAL ANALYSIS | LOOPS | pseudo-isomorphic graph | DISPLACEMENT ISOMORPHISM
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 07/2020, Volume 281, pp. 96 - 105
The problem of the intersection of longest paths consists in determining the size of a smallest subset of vertices of a graph such that every longest path contains at least one vertex of the set... 
MATHEMATICS, APPLIED | NONEMPTY INTERSECTION | PLANAR
Journal Article
Journal of combinatorial theory. Series B, ISSN 0095-8956, 01/2017, Volume 122, pp. 741 - 756
For a loopless multigraph G, the fractional arboricityArb(G) is the maximum of |E(H)||V(H)|−1 over all subgraphs H with at least two vertices. Generalizing the... 
Graph decomposition | Sparse graph | Arboricity | Fractional arboricity | Forest | Discharging method | Nash-Williams Arboricity Formula | Nine Dragon Tree Conjecture | MATHEMATICS | PLANAR GRAPHS | GIRTH | Forests and forestry
Journal Article
Theoretical computer science, ISSN 0304-3975, 08/2015, Volume 593, pp. 160 - 164
Let G be any connected graph on n vertices, n≥2. Let k be any positive integer. Suppose that a fire breaks out at some vertex of G... 
Firefighter problem | Planar graph | Surviving rate | COMPUTER SCIENCE, THEORY & METHODS | Integers | Firefighters | Breaking | Fires | Graphs | Spreads | Mathematical models | Graph theory
Journal Article
Journal of combinatorial theory. Series B, ISSN 0095-8956, 2015, Volume 110, pp. 79 - 89
A k-queue layout of a graph consists of a total order of the vertices, and a partition of the edges into k sets such that no two edges that are in the same set are nested with respect to the vertex ordering... 
Queue number | Graph separators | Track number | Graph layouts | 3D grid drawings | STACK | MATHEMATICS | DIRECTED ACYCLIC GRAPHS | NUMBER | QUEUE LAYOUTS | PLANAR GRAPHS | PAGENUMBER
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 07/2015, Volume 79, Issue 3, pp. 178 - 212
A signed graph [G,Σ] is a graph G together with an assignment of signs + and − to all the edges of G where Σ... 
homomorphism | signed graph | coloring | minor | Hadwiger's conjecture | PROJECTIVE CUBES | COLORINGS | MATHEMATICS | EDGE-COLORED GRAPHS | PLANAR GRAPHS | FLOWS | CONJECTURE | Computer Science | Discrete Mathematics
Journal Article
Journal Article
Discrete mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 17, pp. 5381 - 5392
In this paper, we consider the intersection graph G ( R ) of nontrivial left ideals of a ring R... 
Unordered factorization | Hamiltonian graph | Ideal of a ring | Complete graph | Ring | Planar graph | Connected graph | Bipartite graph | Intersection graph | Eulerian graph | Cycle | Artinian ring | COMMUTATIVE RING | ZERO-DIVISOR GRAPH | MATHEMATICS
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 11/2014, Volume 28, Issue 4, pp. 774 - 786
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 10/2016, Volume 32, Issue 3, pp. 927 - 940
A list assignment of a graph G is a function L that assigns a list L(v) of colors to each vertex $$v\in V(G)$$ v ∈ V ( G ) . An $$(L,d)^*$$ ( L , d... 
Convex and Discrete Geometry | Improper choosability | Planar graphs | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Optimization | Cycle | COLORINGS | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 5/2017, Volume 33, Issue 4, pp. 1354 - 1364
.... A graph G is $$(c_{1},c_{2},\ldots ,c_{k})$$ ( c 1 , c 2 , … , c k ) -colorable if the vertex set can be partitioned into k sets $$V_{1},V_{2},\ldots ,V_{k}$$ V 1 , V 2... 
Improper coloring | Convex and Discrete Geometry | Planar graphs | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Operation Research/Decision Theory | Combinatorics | Optimization | Cycle | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LENGTH | CYCLES
Journal Article
Algorithmica, ISSN 1432-0541, 2018, Volume 81, Issue 5, pp. 1818 - 1843
Journal Article
Applied mathematics and computation, ISSN 0096-3003, 2018, Volume 325, pp. 246 - 251
A strong edge coloring of a graph is a proper edge coloring in which every color class is an induced matching... 
Odd graph | Strong chromatic index | Strong edge coloring | Planar graphs | Maximum average degree | MATHEMATICS, APPLIED | GIRTH
Journal Article
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