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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
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
Journal Article
Algorithmica, ISSN 0178-4617, 12/2015, Volume 73, Issue 4, pp. 673 - 695
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
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
Journal Article
Reviews of Modern Physics, ISSN 0034-6861, 10/2008, Volume 80, Issue 4, pp. 1275 - 1335
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
Journal Article
by Li, Rao
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
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
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
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
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
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 01/2017, Volume 659, pp. 53 - 63
Journal Article
Algorithmica, ISSN 0178-4617, 5/2016, Volume 75, Issue 1, pp. 205 - 217
Journal Article
by Zeng, QH and Hou, JF
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
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
Journal Article