The chromatic number of triangle-free and broom-free graphs in terms of the number of vertices
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DOI: 10.1007/s00010-020-00760-z
Abstract: The Gárfás–Sumner conjecture asks whether for every tree T , the class of (induced) T -free graphs is $$\chi $$ χ -bounded. The conjecture is solved for several special trees, but it is still open… read more here.
Keywords: triangle free; free graphs; number; graph ... See more keywords
Upper bounds on the chromatic number of triangle-free graphs with a forbidden subtree
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DOI: 10.1007/s10878-015-9929-z
Abstract: Gyárfás conjectured that for a given forest F, there exists an integer function f(F, x) such that $$\chi (G)\le f(F,\omega (G))$$χ(G)≤f(F,ω(G)) for each F-free graph G, where $$\omega (G)$$ω(G) is the clique number of G. The… read more here.
Keywords: triangle free; free graph; upper bounds; free free ... See more keywords
Random independent sets in triangle-free graphs
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DOI: 10.1017/fms.2025.10112
Abstract: Abstract We establish several new results on the existence of probability distributions on the independent sets in triangle-free graphs where each vertex is present with a given probability. This setting was introduced and studied under… read more here.
Keywords: number; independent sets; sets triangle; triangle free ... See more keywords
Triangle-free Graphs with Three Positive Eigenvalues
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DOI: 10.1142/s1005386724000397
Abstract: A graph [Formula: see text] is called triangle-free if [Formula: see text] does not contain any triangle as its induced subgraph. Let [Formula: see text] be the set of triangle-free graphs of order [Formula: see… read more here.
Keywords: three positive; see text; triangle free; formula see ... See more keywords