Pancyclicity of claw-free hamiltonian 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...
متن کاملPancyclicity of 4-Connected, Claw-Free, P10-Free Graphs
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...
متن کاملPancyclicity of 4-connected {claw, generalized bull}-free graphs
A graph G is pancyclic if it contains cycles of each length `, 3 ≤ ` ≤ |V (G)|. The generalized bull B(i, j) is obtained by associating one endpoint of each of the paths Pi+1 and Pj+1 with distinct vertices of a triangle. Gould, Luczak and Pfender [4] showed that if G is a 3-connected {K1,3, B(i, j)}-free graph with i + j = 4 then G is pancyclic. In this paper, we prove that every 4-connected, ...
متن کاملHamiltonian N2-locally connected claw-free graphs
A graph G is N2-locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryjác̆ek conjectured that every 3-connected N2-locally connected claw-free graph is hamiltonian. This conjecture is proved in this note.
متن کاملUnifying Results on Hamiltonian Claw-free Graphs
This work was motivated by many (recent) papers on hamiltonicity of claw-free graphs, i.e. graphs that do not contain K 1;3 as an induced sub-graph. By combining ideas from these papers with some new observations, we unify several of the existing suuciency results, using a new suucient condition consisting of seven subconditions. If each pair of vertices at distance two of a 2-connected claw-fr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00278-7