The maximum number of edges in 2K2-free graphs of bounded degree
Discrete Mathematics
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Radius two trees specify &khgr;-bounded classes
Journal of Graph Theory
Dominating subgraphs in graphs with some forbidden structures
Discrete Mathematics
The Ramsey number R(3, t) has order of magnitude t2/log t
Random Structures & Algorithms
Colouring graphs with prescribed induced cycle lengths
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Three-colourbility and forbidden subgraphs. II: polynomial algorithms
Discrete Mathematics
On the Structure of Dense Triangle-Free Graphs
Combinatorics, Probability and Computing
Colouring vertices of triangle-free graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Coloring graphs without short cycles and long induced paths
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Determining the chromatic number of triangle-free 2P3-free graphs in polynomial time
Theoretical Computer Science
Coloring graphs without short cycles and long induced paths
Discrete Applied Mathematics
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The relation of chromatic aspects and the existence of certain induced subgraphs of a triangle-free graph will be investigated. Based on a characterization statement of Pach, some results on the chromatic number of triangle-free graphs with certain forbidden induced subgraphs will be refined by describing their structure in terms of homomorphisms. In particular, we introduce chordal triangle-free graphs as a natural superclass of chordal bipartite graphs and describe the structure of the maximal triangle-free members. Finally, we improve on the upper bound for the chromatic number of triangle-free sK2-free graphs by 1 for s ≥ 2, giving the tight bound for s = 3.