A graph ?$G$? is hypohamiltonian if ?$G$? is non-hamiltonian and ?$G - v$? is hamiltonian for every ?$v \in V(G$)?. 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 graphs of order 19. We also extend their results in the cubic case. Furthermore, we show that (i) the smallest graph of girth 6 has order 25, (ii) the smallest planar graph has order at least 23, (iii) the smallest cubic planar graph has order at least 54, and (iv) the smallest cubic planar graph of girth 5 with non-trivial automorphism group has order 78.

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URN

URN:NBN:SI:DOC-PKP5T2IZ

COBISSID

18354521

Added

29.05.2020

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Citation

APA:

Goedgebeur, Jan, Zamfirescu, Carol T. (2017). Improved bounds for hypohamiltonian graphs. Ars mathematica contemporanea, volume 13, issue 2, str. 235-257. URN:NBN:SI:DOC-PKP5T2IZ from http://www.dlib.si

MLA:

Goedgebeur, Jan, Zamfirescu, Carol T.. "Improved bounds for hypohamiltonian graphs." Ars mathematica contemporanea volume 13. issue 2 (2017) str. 235-257.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-PKP5T2IZ>

Ars mathematica contemporanea
2008-
(Assembly record)