Minimal 2-connected non-hamiltonian claw-free graphs
نویسندگان
چکیده
منابع مشابه
Hamiltonian 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 کاملClaw-free 3-connected P11-free graphs are hamiltonian
We show that every 3-connected claw-free graph which contains no induced copy of P11 is hamiltonian. Since there exist non-hamiltonian 3-connected claw-free graphs without induced copies of P12 this result is, in a way, best possible. 1. Statement of the main result A graph G is {H1, H2, . . . Hk}-free if G contains no induced subgraphs isomorphic to any of the graphs Hi, i = 1, 2, . . . , k. A...
متن کاملHamiltonian properties of almost locally connected claw-free graphs
A vertex v of a graph G is locally connected if the set of neighbors N(v) of v induces a connected subgraph in G. Let B(G) denote the set of vertices of G that are not locally connected. Then G is almost locally connected if B(G) is an independent set and for any x ∈ B(G), there is a vertex y in V (G) \ {x} such that N(x) ∪ {y} induces a connected subgraph of G. The main result of this paper is...
متن کاملHamiltonian cycles in 3-connected Claw-free graphs
It is shown that every 3-connected claw-free graph having at most 6 − 7 vertices is hamiltonian, where is the minimum degree. c © 2002 Elsevier Science B.V. All rights reserved.
متن کاملMinimal Claw-Free Graphs
A graph G is a minimal claw-free graph (m.c.f. graph) if it contains no K1,3 (claw) as an induced subgraph and if, for each edge e of G, G − e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs. MSC 2000: 05C75, 05C07
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: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00093-4