Zs. Tuza

TL;DR: This question was motivated by practical problems in scheduling and VLSI theory and its complexity status for interval graphs and for graphs with a bounded treewidth is investigated.

TL;DR: 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.

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.

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.

TL;DR: This paper proves special cases of the following conjecture: for any fixed tree T there exists a natural number f = f (T) to that every triangle-free graph of chromaticnumber f(T) contains T as an induced subgraph.