Pancyclicity in claw-free graphs
نویسندگان
چکیده
منابع مشابه
Pancyclicity in claw-free graphs
In this paper, we present several conditions for K1;3-free graphs, which guarantee the graph is subpancyclic. In particular, we show that every K1;3-free graph with a minimum degree sum 2 ¿ 2 √ 3n+ 1 − 4; every {K1;3; P7}-free graph with 2 ¿ 9; every {K1;3; Z4}-free graph with 2 ¿ 9; and every K1;3-free graph with maximum degree , diam(G)¡ ( +6)=4 and 2 ¿ 9 is subpancyclic. c © 2002 Elsevier Sc...
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A graph G is said to be pancyclic if G contains cycles of all lengths from 3 to |V (G)|. We show that if G is 4-connected, claw-free, and P10-free, then G is either pancyclic or it is the line graph of the Petersen graph. This implies that every 4-connected, claw-free, P9-free graph is pancyclic, which is best possible and extends a result of Gould et al. Pancyclicity in 3-connected graphs: Pai...
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In this paper we prove that if G is a connected claw-free graph with three pairwise non-adjacent vertices, with chromatic number χ and clique number ω, then χ ≤ 2ω and the same for the complement of G. We also prove that the choice number of G is at most 2ω, except possibly in the case when G can be obtained from a subgraph of the Schläfli graph by replicating vertices. Finally, we show that th...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00465-4