The number of maximal independent sets in connected triangle-free graphs
نویسندگان
چکیده
منابع مشابه
The independent domination number of maximal triangle-free graphs
A triangle-free graph is maximal if the addition of any edge produces a triangle. A set S of vertices in a graph G is called an independent dominating set if S is both an independent and a dominating set of G. The independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. In this paper, we show that i(G) ≤ δ(G) ≤ n 2 for maximal triangle-free graph...
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Ajtai, Komlós, and Szemerédi proved that for sufficiently large t every trianglefree graph with n vertices and average degree t has an independent set of size at least n 100t log t. We extend this by proving that the number of independent sets in such a graph is at least 2 1 2400 n t log . This result is sharp for infinitely many t, n apart from the constant. An easy consequence of our result i...
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A Turán connected graph TCn,α is obtained from α cliques of size b αc or d αe by joining all cliques by an edge to one central vertex in one of the larger cliques. The graph TCn,α was shown recently by Bruyère and Mélot to maximise the number of independent sets among connected graphs of order n and independence number α. We prove a generalisation of this result by showing that TCn,α in fact ma...
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Let G be a simple undirected graph. Denote by mi(G) (respectively, xi(G)) the number of maximal (respectively, maximum) independent sets in G. In this paper we determine the third and fouth largest value of mi(G) among all graphs of order n. Moreover, the extremal graphs achieving these values are also determined. Mathematics Subject Classification: 05C35, 05C69, 68R10
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)90057-2