Journal ArticleDOI
Dominating cliques in P5-free graphs
Gábor Bacsó,Zs. Tuza +1 more
TLDR
In this paper, the problem of finding any given type of connected dominating sets in all members of a classG of graphs can be reduced to the graphsG∈G that have a cut-vertex or do not contain any cutsetS dominated by somes∈S.Abstract:
All induced connected subgraphs of a graphG contain a dominating set of pair-wise adjacent vertices if and only if there is no induced subgraph isomorphic to a path or a cycle of five vertices inG. Moreover, the problem of finding any given type of connected dominating sets in all members of a classG of graphs can be reduced to the graphsG∈G that have a cut-vertex or do not contain any cutsetS dominated by somes∈S.read more
Citations
More filters
Journal ArticleDOI
Deciding k -Colorability of P 5 -Free Graphs in Polynomial Time
TL;DR: In this paper, it was shown that for every fixed integer k, there exists a polynomial-time algorithm for determining whether a P5-free graph admits a k-coloring, and finding one, if it does.
Journal ArticleDOI
Vertex Colouring and Forbidden Subgraphs – A Survey
Bert Randerath,Ingo Schiermeyer +1 more
TL;DR: This work surveys results on vertex colourings of graphs defined in terms of forbidden induced subgraph conditions in order to obtain useful results from a graph coloring formulation of his problem.
Precoloring extension. ii. graphs classes related to bipartite graphs
Mihály Hujter,Zs. Tuza +1 more
TL;DR: In this paper, the complexity status of precoloring extendibility on some graph classes which are related to bipartite graphs was investigated, giving a complete solution for graphs with co-chromatic number 2, i.e., admitting a parti- tion V = V 1 (V 2 of the vertex set V such that each V i induces a complete subgraph or an independent set.
Journal ArticleDOI
3-Colorability ∈ P for P 6 -free graphs
Bert Randerath,Ingo Schiermeyer +1 more
TL;DR: In this paper, it was shown that 3-colorability can be decided in polynomial time for the class of P6-free graphs with bounded dominating subgraphs.
Journal ArticleDOI
Precoloring Extension III: Classes of Perfect Graphs
Mihály Hujter,Zsolt Tuza +1 more
TL;DR: Here it is investigated the complexity status of precolouring extendibility on some classes of perfect graphs, giving good characterizations that lead to algorithms with linear or polynomial running time.
References
More filters
Journal ArticleDOI
On a property of the class of n-colorable graphs
TL;DR: In this paper, a necessary and sufficient condition for a graph to be n-colorable was derived from a lower bound on the chromatic number of points in a complete subgraph.
Journal ArticleDOI
Star-cutsets and perfect graphs
TL;DR: This work first establishes a certain property of minimal imperfect graphs and then uses it to generate large classes of perfect graphs, which are then used to establish and generate large numbers of minimal perfect graphs.
Journal ArticleDOI
The maximum number of edges in 2 K 2 -free graphs of bounded degree
TL;DR: It is shown that if G is 2K2-free and has maximum degree Δ(G)=D, then G has at most 5D24 edges if D is even, and this bound can be improved to (5D2−2D+1)4.
Journal ArticleDOI
On domination problems for permutation and other graphs
TL;DR: An algorithm with time bound O ( n 2 ) for the weighted independent domination problem on permutation graphs and an investigation of (weighted) dominating clique problems for several graph classes including an NP-completeness result for weakly triangulated graphs as well as polynomial time bounds are given.