Hamiltonicity of connected domination critical graphs
Citation
Kaemawichanurat, P. and Caccetta, L. and Ananchuen, W. 2018. Hamiltonicity of connected domination critical graphs. Ars Combinatoria. 136: pp. 127-151.
Source Title
Ars Combinatoria
ISSN
School
School of Electrical Engineering, Computing and Mathematical Science (EECMS)
Collection
Abstract
© 2018 Charles Babbage Research Centre. All rights reserved. A graph G is said to be k-yc-critical if the connected domination number yc(G) of G is k and yc(G + uv) < k for every uv ? E(G). The problem of interest for a positive integer I > 2 is to determine whether or not l-connected k-yc-critical graphs are Hamiltonian. In this paper, for I > 2, we prove that if k - 1,2 or 3, then every l-connected k-yc-critical graph is Hamiltonian. We further show that, for n > (k - 1)k + 3, the class of i-connected Jt-yc-critical non-Hamiltonian graphs of order n is empty if and only if k = 1,2 or 3.
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