Panconnectivity of locally connected 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 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 کاملSpanning eulerian subgraphs in N -locally connected claw-free graphs
A graph G is Nm-locally connected if for every vertex v in G, the vertices not equal to v and with distance at most m to v induce a connected subgraph in G. We show that both connected N2-locally connected claw-free graph and 3-edge-connected N3-locally connected claw-free graph have connected even [2, 4]-factors, which settle a conjecture by Li in [6].
متن کاملSpanning eulerian subgraphs in N2-locally connected claw-free graphs
A graph G is Nm-locally connected if for every vertex v in G, the vertices not equal to v and with distance at most m to v induce a connected subgraph in G. We show that both connectedN2-locally connected claw-free graph and 3-edge-connected N3-locally connected claw-free graph have connected even [2, 4]-factors, which settle a conjecture by Li in [6].
متن کاملQuadrangularly 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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00010-2