A Fan-type condition for claw-free graphs to be Hamiltonian
نویسندگان
چکیده
منابع مشابه
A Fan-type condition for Hamiltonian graphs
For two non-adjacent vertices u: v in a graph G, we use a(u~ v) to denote the ma."\.imum cardinality of an independent vertex set of G containing both u and v. In this paper, we prove that if G is a 2-connected graph of order n and max{d{u),d(v}} ~ ~ for each pair of nonadjacent vertices Lt. v of G with 1 ::; IN( u) nN( v) I < a(u, v) -1, then either G is Hamiltonian or else G belongs to a fami...
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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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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...
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Let A be a ®nite abelian group and G be a digraph. The boundary of a function f : E G 7! A is a function q f : V G 7! A given by q f v Pe leaving v f eÿ P e entering v f e. The graph G is A-connected if for every b : V G 7! A with P v AV G b v 0, there is a function f : E G 7! Aÿ f0g such that q f b. In [J. Combinatorial Theory, Ser. B 56 (1992) 165±182], Jaeger et al showed th...
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A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. In this note, we prove that claw-free graphs with minimum degree at least 3 are not uniquely Hamiltonian. We also show that this is best possible by exhibiting uniquely Hamiltonian claw-free graphs with minimum degree 2 and arbitrary maximum degree. Finally, we show that a construction due to Entringer and Swart can b...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00341-6