On hypohamiltonian graphs
نویسندگان
چکیده
منابع مشابه
New 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 کاملSmall 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...
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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...
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A graph is hypohamiltonian if it is not Hamiltonian, but the deletion of any single vertex gives a Hamiltonian graph. Until now, the smallest known planar hypohamiltonian graph had 42 vertices, a result due to Araya and Wiener. That result is here improved upon by 25 planar hypohamiltonian graphs of order 40, which are found through computer-aided generation of certain families of planar graphs...
متن کاملOn Cubic Planar Hypohamiltonian and Hypotraceable Graphs
We present a cubic planar hypohamiltonian graph on 70 vertices, improving the best known bound of 94 by Thomassen and derive some consequences concerning longest paths and cycles of planar 3-connected graphs. We also show that cubic planar hypohamiltonian graphs on n vertices exist for every even number n ≥ 86 and that cubic planar hypotraceable graphs exist on n vertices for every even number ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1974
ISSN: 0012-365X
DOI: 10.1016/0012-365x(74)90128-9