منابع مشابه
Small Hypohamiltonian Graphs
A graph G is said to be hypohamiltonian if G is not hamiltonian but for each v ∈ V (G) the vertex deleted subgraph G − v is hamiltonian. In this paper we show that there is no hypohamiltonian graph on 17 vertices and thereby complete the answer to the question, “for which values of n do there exist hypohamiltonian graphs on n vertices?”. In addition we present an exhaustive list of hypohamilton...
متن کاملPlanar hypohamiltonian graphs
A graph is called hypohamiltonian if it is not hamiltonian but, when omitting an arbitrary vertex, it becomes hamiltonian. The smallest hypohamiltonian graph is the famous Petersen graph (found by Kempe in 1886) on 10 vertices. In 1963, Sousselier posed a problem of recreational nature, and thus began the study of hypohamiltonian graphs. Many authors followed, in particular Thomassen with a ser...
متن کاملNew results on hypohamiltonian and almost hypohamiltonian graphs
Consider a non-hamiltonian graph G. G is hypohamiltonian if for every vertex v in G, the graph G − v is hamiltonian. G is almost hypohamiltonian if there exists a vertex w in G such that G−w is non-hamiltonian, and G− v is hamiltonian for every vertex v 6= w. McKay asked in [J. Graph Theory, doi: 10.1002/jgt.22043] whether infinitely many planar cubic hypohamiltonian graphs of girth 5 exist. We...
متن کاملImproved bounds for hypohamiltonian graphs
A graph G is hypohamiltonian if G is non-hamiltonian and G − v is hamiltonian for every v ∈ V (G). In the following, every graph is assumed to be hypohamiltonian. Aldred, Wormald, and McKay gave a list of all graphs of order at most 17. In this article, we present an algorithm to generate all graphs of a given order and apply it to prove that there exist exactly 14 graphs of order 18 and 34 gra...
متن کاملHypohamiltonian Graphs and their Crossing Number
We prove that for every k > 0 there is an integer n0(k) such that, for every n > n0, there exists a hypohamiltonian graph which has order n and crossing number k.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.01.009