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Journals and Conferences
We present a planar hypohamiltonian graph on 48 vertices, and derive some consequences. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 338–342, 2007
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… (More)
In 2003, Cavicchioli et al. corrected an omission in the statement and proof of Fiorini’s theorem from 1983 on hypohamiltonian snarks. However, their version of this theorem contains an unattainable… (More)
A graph G is almost hypohamiltonian if G is nonhamiltonian, there exists a vertex w such that G − w is nonhamiltonian, and for any vertex v 6= w the graph G − v is hamiltonian. We prove the existence… (More)
We give a brief introduction to the topic of twodimensional acute triangulations, mention results on related areas, survey existing achievements – with emphasis on recent activity – and list related… (More)
This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher… (More)
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… (More)
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.
We investigate here the hamiltonicity and traceability of a class of polytopes generalizing pyramids, prisms, and polytopes with Halin 1-skeleta.
We call a graph G a platypus if G is non-hamiltonian, and for any vertex v in G, the graph G− v is traceable. Every hypohamiltonian and every hypotraceable graph is a platypus, but there exist… (More)