Graphs and Combinatorics, ISSN 0911-0119, 1/2018, Volume 34, Issue 1, pp. 97 - 107

The class of $$2K_{2}$$ 2K2 -free graphs and its various subclasses have been studied in a variety of contexts. In this paper, we are concerned with the...

(P_3 \cup P_2)$$ ( P 3 ∪ P 2 ) -free graphs | 05C17 | Mathematics | Colouring | Clique number | Diamond | Engineering Design | Perfect graphs | Combinatorics | Chromatic number | 2K_{2}$$ 2 K 2 -free graphs | 05C15 | P | free graphs | 2 K | MATHEMATICS | 2K-free graphs | SUBGRAPHS | (P-3 boolean OR P-2)-free graphs

(P_3 \cup P_2)$$ ( P 3 ∪ P 2 ) -free graphs | 05C17 | Mathematics | Colouring | Clique number | Diamond | Engineering Design | Perfect graphs | Combinatorics | Chromatic number | 2K_{2}$$ 2 K 2 -free graphs | 05C15 | P | free graphs | 2 K | MATHEMATICS | 2K-free graphs | SUBGRAPHS | (P-3 boolean OR P-2)-free graphs

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 09/2017, Volume 33, Issue 5, pp. 1095 - 1101

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 18, pp. 4280 - 4285

A graph G is called { H 1 , H 2 , … , H k } -free if G contains no induced subgraph isomorphic to any H i , 1 ⩽ i ⩽ k . If G is a complete graph, we set NC = |...

Hamilton path | [formula omitted]-free graph | Neighborhood union | e }-free graph | K | MATHEMATICS | neighborhood union | K-1,K-4, K-1,K-4 + e)-free graph

Hamilton path | [formula omitted]-free graph | Neighborhood union | e }-free graph | K | MATHEMATICS | neighborhood union | K-1,K-4, K-1,K-4 + e)-free graph

Journal Article

Algorithmica, ISSN 0178-4617, 12/2015, Volume 73, Issue 4, pp. 673 - 695

A graph drawn in the plane with $$n$$ n vertices is $$k$$ k -fan-crossing free for $$k \geqslant 2$$ k ⩾ 2 if there are no $$k+1$$ k + 1 edges $$g,e_1,\ldots ,...

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Graph drawing | Theory of Computation | K-planar graphs | Algorithm Analysis and Problem Complexity | Crossing number | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | QUASI-PLANAR GRAPHS | Computer science

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Graph drawing | Theory of Computation | K-planar graphs | Algorithm Analysis and Problem Complexity | Crossing number | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | QUASI-PLANAR GRAPHS | Computer science

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 03/2015, Volume 184, pp. 114 - 121

In VCP 4 problem, it is asked to find a set S⊆V of minimum size such that G[V\S] contains no path on 4 vertices, in a given graph G=(V,E). We prove that it is...

Approximation algorithm | K 1 4 -free graph | P 4 vertex cover | Regular graph | Algorithms

Approximation algorithm | K 1 4 -free graph | P 4 vertex cover | Regular graph | Algorithms

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2013, Volume 161, Issue 1-2, pp. 140 - 150

The k-Coloring problem is to test whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. If a graph G...

Forbidden induced subgraph | Polynomial-time algorithm | Graph coloring | Linear forest | NP-COMPLETENESS | COLORING GRAPHS | MATHEMATICS, APPLIED | 3-COLORABILITY | K-COLORABILITY | COMPLEXITY | ALGORITHM

Forbidden induced subgraph | Polynomial-time algorithm | Graph coloring | Linear forest | NP-COMPLETENESS | COLORING GRAPHS | MATHEMATICS, APPLIED | 3-COLORABILITY | K-COLORABILITY | COMPLEXITY | ALGORITHM

Journal Article

Reviews of Modern Physics, ISSN 0034-6861, 10/2008, Volume 80, Issue 4, pp. 1275 - 1335

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects...

STATISTICAL-MECHANICS | PHYSICS, MULTIDISCIPLINARY | SMALL-WORLD | FERROMAGNETIC ISING-MODEL | EXACTLY SOLVABLE MODEL | diseases | ORDER PHASE-TRANSITION | complex networks | RANDOM GRAPHS | synchronisation | ecology | K-CORE | SPIN MODELS | Ising model | POTTS-MODEL | CRITICAL-BEHAVIOR | Network architecture | Evaluation | Usage | Graph theory | Phase transformations (Statistical physics) | Analysis

STATISTICAL-MECHANICS | PHYSICS, MULTIDISCIPLINARY | SMALL-WORLD | FERROMAGNETIC ISING-MODEL | EXACTLY SOLVABLE MODEL | diseases | ORDER PHASE-TRANSITION | complex networks | RANDOM GRAPHS | synchronisation | ecology | K-CORE | SPIN MODELS | Ising model | POTTS-MODEL | CRITICAL-BEHAVIOR | Network architecture | Evaluation | Usage | Graph theory | Phase transformations (Statistical physics) | Analysis

Journal Article

数学学报：英文版, ISSN 1439-8516, 2012, Volume 28, Issue 1, pp. 171 - 182

Given a vertex v of a graph G the second order degree of v denoted as d2（v） is defined as the number of vertices at distance 2 from v. In this paper we address...

二阶 | 顶点 | 平面图 | 充分条件 | 图形显示 | 距离 | 05C75 | K 4 − -free graph | 05C12 | planar graphs | Mathematics, general | Mathematics | Second order degree | free graph | MATHEMATICS | K-4(-)-free graph | MATHEMATICS, APPLIED | TREES | Studies | Graph theory | Graphs

二阶 | 顶点 | 平面图 | 充分条件 | 图形显示 | 距离 | 05C75 | K 4 − -free graph | 05C12 | planar graphs | Mathematics, general | Mathematics | Second order degree | free graph | MATHEMATICS | K-4(-)-free graph | MATHEMATICS, APPLIED | TREES | Studies | Graph theory | Graphs

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2004, Volume 287, Issue 1, pp. 69 - 76

A graph G is called { H 1 , H 2 , … , H k } -free if G contains no induced subgraph isomorphic to any H i , 1 ⩽ i ⩽ k . Let G be a 2-connected { K 1 , 4 , K 1...

[formula omitted]-free graphs | Hamiltonicity | e}-free graphs | K

[formula omitted]-free graphs | Hamiltonicity | e}-free graphs | K

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 1/2018, Volume 34, Issue 1, pp. 85 - 95

Given a graph H, we say a graph G is H-saturated if G does not contain H as a subgraph and the addition of any edge $$e'\not \in E(G)$$ e′∉E(G) results in H as...

Edge spectrum | K_4-e$$ K 4 - e | Saturated | Mathematics | Engineering Design | K_t-e$$ K t - e | Combinatorics | e | MATHEMATICS | K-t - e | K-4 - e

Edge spectrum | K_4-e$$ K 4 - e | Saturated | Mathematics | Engineering Design | K_t-e$$ K t - e | Combinatorics | e | MATHEMATICS | K-t - e | K-4 - e

Journal Article

Discrete Mathematics, ISSN 0012-365X, 02/2013, Volume 313, Issue 4, pp. 406 - 421

It is well known that every planar graph contains a vertex of degree at most 5. A theorem of Kotzig states that every 3-connected planar graph contains an edge...

Light subgraphs | Plane graphs | Weight of subgraph | POLYHEDRAL GRAPHS | K-1,K-R-FREE GRAPHS | 3-CONNECTED GRAPHS | 2 THEOREMS | PATHS | CYCLIC CHROMATIC NUMBER | MATHEMATICS | BOUNDARY VERTICES | RESTRICTED DEGREES | 2-DIMENSIONAL MANIFOLDS | LIST EDGE

Light subgraphs | Plane graphs | Weight of subgraph | POLYHEDRAL GRAPHS | K-1,K-R-FREE GRAPHS | 3-CONNECTED GRAPHS | 2 THEOREMS | PATHS | CYCLIC CHROMATIC NUMBER | MATHEMATICS | BOUNDARY VERTICES | RESTRICTED DEGREES | 2-DIMENSIONAL MANIFOLDS | LIST EDGE

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 9/2014, Volume 30, Issue 5, pp. 1261 - 1269

Lai, Shao and Zhan (J Graph Theory 48:142–146, 2005) showed that every 3-connected N 2-locally connected claw-free graph is Hamiltonian. In this paper, we...

Singular edge | Locally disconnected vertex | Claw-free graph | Hamiltonicity | Mathematics | Engineering Design | Combinatorics | Singular k -cycle (property) | Singular k-cycle (property) | MATHEMATICS | CYCLES | Graph theory | Graphs | Triangles | Combinatorial analysis | Disengaging

Singular edge | Locally disconnected vertex | Claw-free graph | Hamiltonicity | Mathematics | Engineering Design | Combinatorics | Singular k -cycle (property) | Singular k-cycle (property) | MATHEMATICS | CYCLES | Graph theory | Graphs | Triangles | Combinatorial analysis | Disengaging

Journal Article

IEEE Transactions on Computers, ISSN 0018-9340, 06/2015, Volume 64, Issue 6, pp. 1622 - 1632

(t, k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least k faulty processors be identified and repaired in each iteration...

Fault diagnosis | Program processors | Computational modeling | Educational institutions | Sequential diagnosis | Circuit faults | Multiprocessing systems | Conditional fault diagnosis | fault-tolerance | multiprocessor systems | sequential diagnosis | MM∗ model | system-level diagnosis | (t,k)-diagnosis | MM model | HYPERCUBES | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | (t, k)-diagnosis | NETWORKS | DIAGNOSABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Fault tolerance (Computers) | Graph theory | Computer-generated environments | Research | Computer simulation | Lower bounds | Toruses | Graphs | Diagnosis | Transaction processing | Processors | Symmetry

Fault diagnosis | Program processors | Computational modeling | Educational institutions | Sequential diagnosis | Circuit faults | Multiprocessing systems | Conditional fault diagnosis | fault-tolerance | multiprocessor systems | sequential diagnosis | MM∗ model | system-level diagnosis | (t,k)-diagnosis | MM model | HYPERCUBES | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | (t, k)-diagnosis | NETWORKS | DIAGNOSABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Fault tolerance (Computers) | Graph theory | Computer-generated environments | Research | Computer simulation | Lower bounds | Toruses | Graphs | Diagnosis | Transaction processing | Processors | Symmetry

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 07/2019, Volume 776, pp. 64 - 74

A (δ≥k1,δ≥k2)-partition of a graph G is a vertex-partition (V1,V2) of G into two non-empty sets satisfying that δ(G[Vi])≥ki for i=1,2. We determine, for all...

2-partition | Minimum degree | [formula omitted]-complete | Polynomial time | NP-complete | Computer science | Logic | Mathematics

2-partition | Minimum degree | [formula omitted]-complete | Polynomial time | NP-complete | Computer science | Logic | Mathematics

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 01/2017, Volume 659, pp. 53 - 63

Many large-scale multiprocessor or multi-computer systems take interconnection networks as underlying topologies. Fault diagnosis is especially important to...

MM model | [formula omitted]-star graphs | PMC model | The g-good-neighbor diagnosability | Diagnosability | Multiprocessor systems | (n,k)-star graphs | BC NETWORKS | COMPARISON DIAGNOSIS MODEL | CONDITIONAL DIAGNOSABILITY | RELIABILITY | FAULT-TOLERANCE | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | SHUFFLE-CUBES | Computer science | Multiprocessing | Analysis | Fault diagnosis | Networks | Computer simulation | Fault detection | Interconnection | Graphs | Mathematical models | Topology

MM model | [formula omitted]-star graphs | PMC model | The g-good-neighbor diagnosability | Diagnosability | Multiprocessor systems | (n,k)-star graphs | BC NETWORKS | COMPARISON DIAGNOSIS MODEL | CONDITIONAL DIAGNOSABILITY | RELIABILITY | FAULT-TOLERANCE | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | SHUFFLE-CUBES | Computer science | Multiprocessing | Analysis | Fault diagnosis | Networks | Computer simulation | Fault detection | Interconnection | Graphs | Mathematical models | Topology

Journal Article

Algorithmica, ISSN 0178-4617, 5/2016, Volume 75, Issue 1, pp. 205 - 217

Let $$G$$ G be a connected $$P_k$$ P k -free graph, $$k \ge 4$$ k ≥ 4 . We show that $$G$$ G admits a connected dominating set that induces either a...

05C75 | Connected domination | Theory of Computation | Computational complexity | P_k$$ P k -free graph | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | 05C69 | Algorithm Analysis and Problem Complexity | 05C38

05C75 | Connected domination | Theory of Computation | Computational complexity | P_k$$ P k -free graph | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | 05C69 | Algorithm Analysis and Problem Complexity | 05C38

Journal Article

ARS MATHEMATICA CONTEMPORANEA, ISSN 1855-3966, 2018, Volume 15, Issue 1, pp. 147 - 160

For a graph G, let f(G) denote the maximum number of edges in a bipartite subgraph of G. For an integer m >= 1 and for a set H of graphs, let f(m, H) denote...

MATHEMATICS | H-free graph | MATHEMATICS, APPLIED | NUMBER | partition | maximum cut | BIPARTITE SUBGRAPHS | BOUNDS | JUDICIOUS K-PARTITIONS | TRIANGLE-FREE GRAPHS

MATHEMATICS | H-free graph | MATHEMATICS, APPLIED | NUMBER | partition | maximum cut | BIPARTITE SUBGRAPHS | BOUNDS | JUDICIOUS K-PARTITIONS | TRIANGLE-FREE GRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 04/2014, Volume 167, pp. 107 - 120

For an integer k≥1, a graph G is k-colorable if there exists a mapping c:VG→{1,…,k} such that c(u)≠c(v) whenever u and v are two adjacent vertices. For a fixed...

Forbidden induced subgraph | Girth | Graph coloring | MATHEMATICS, APPLIED | TIME | LOGIC | TRIANGLE-FREE GRAPHS | NP-COMPLETENESS | K-COLORABILITY | COMPLEXITY | P-6-FREE | CLIQUE-WIDTH | FORBIDDEN SUBGRAPHS | Integers | Coloring | Lower bounds | Mathematical analysis | Graphs | Polynomials | Mapping

Forbidden induced subgraph | Girth | Graph coloring | MATHEMATICS, APPLIED | TIME | LOGIC | TRIANGLE-FREE GRAPHS | NP-COMPLETENESS | K-COLORABILITY | COMPLEXITY | P-6-FREE | CLIQUE-WIDTH | FORBIDDEN SUBGRAPHS | Integers | Coloring | Lower bounds | Mathematical analysis | Graphs | Polynomials | Mapping

Journal Article