Quadrangularly connected claw-free graphs
نویسندگان
چکیده
منابع مشابه
Quadrangularly connected claw-free graphs
A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of l-cycles (3 ≤ l ≤ 4) C1, C2, ..., Cr such that e1 ∈ E(C1) and e2 ∈ E(Cr) and E(Ci) ∩ E(Ci+1) 6= ∅ for i = 1, 2, ..., r − 1. In this paper, we show that every quadrangularly connected claw-free graph without vertices of degree 1, which does not contain an induced subgraph H isomorphic to eithe...
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.
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A graph G is k-Hamilton-connected (k-hamiltonian) if G−X is Hamilton-connected (hamiltonian) for every setX ⊂ V (G) with |X| = k. In the paper, we prove that (i) every 5-connected claw-free graph with minimum degree at least 6 is 1Hamilton-connected, (ii) every 4-connected claw-free hourglass-free graph is 1-Hamilton-connected. As a byproduct, we also show that every 5-connected line graph with...
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Kuipers and Veldman conjectured that any 3-connected claw-free graph with order ν and minimum degree δ ≥ ν+6 10 is Hamiltonian for ν sufficiently large. In this paper, we prove that if H is a 3-connected claw-free graph with sufficiently large order ν, and if δ(H) ≥ ν+5 10 , then either H is hamiltonian, or δ(H) = ν+5 10 and the Ryjác̆ek’s closure cl(H) of H is the line graph of a graph obtained...
متن کاملCritical graphs for subpancyclicity of 3-connected claw-free graphs
Let Fk be the family of graphs G such that all sufficiently large k-connected claw-free graphs which contain no induced copies of G are subpancyclic. We show that for every k≥3 the family F1k is infinite and make the first step toward the complete characterization of the family F3. 2009 Wiley Periodicals, Inc. J Graph Theory 62: 263–278, 2009 Contract grant sponsor: KBN (T. L.); Contract grant ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.07.034