Cycle-maximal triangle-free graphs
نویسندگان
چکیده
منابع مشابه
Cycle-maximal triangle-free graphs
We conjecture that the balanced complete bipartite graph K⌊n/2⌋,⌈n/2⌉ contains more cycles than any other n-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and u...
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We show that a maximal triangle-free graph on n vertices with minimum degree δ contains an independent set of 3δ − n vertices which have identical neighborhoods. This yields a simple proof that if the binding number of a graph is at least 3/2 then it has a triangle. This was conjectured originally by Woodall. We consider finite undirected graphs on n vertices with minimum degree δ. A maximal tr...
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An induced matching in a graph is a set of edges whose endpoints induce a 1-regular subgraph. It is known that every n-vertex graph has at most 10 ≈ 1.5849 maximal induced matchings, and this bound is best possible. We prove that every n-vertex triangle-free graph has at most 3 ≈ 1.4423 maximal induced matchings, and this bound is attained by every disjoint union of copies of the complete bipar...
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Scott conjectured in [6] that the class of graphs with no induced subdivision of a given graph is χ-bounded. We verify his conjecture for maximal triangle-free graphs. Let F be a graph. We denote by Forb∗(F ) the class of graphs with no induced subdivision of F . A class G of graphs is χ-bounded if there exists a function f such that every graph G of G satisfies χ(G) ≤ f(ω(G)), where χ and ω re...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2015
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.10.002