Pfaffian orientation and enumeration of perfect matchings for some Cartesian products of graphs.
Lin, Feng-Gen, Zhang, Lian-Zhu (2009)
The Electronic Journal of Combinatorics [electronic only]
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Lin, Feng-Gen, Zhang, Lian-Zhu (2009)
The Electronic Journal of Combinatorics [electronic only]
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Bakonyi, Mihály, Varness, Erik M. (1995)
International Journal of Mathematics and Mathematical Sciences
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Judith Keijsper, Meike Tewes (2002)
Discussiones Mathematicae Graph Theory
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A β-perfect graph is a simple graph G such that χ(G') = β(G') for every induced subgraph G' of G, where χ(G') is the chromatic number of G', and β(G') is defined as the maximum over all induced subgraphs H of G' of the minimum vertex degree in H plus 1 (i.e., δ(H)+1). The vertices of a β-perfect graph G can be coloured with χ(G) colours in polynomial time (greedily). The main purpose of this paper is to give necessary and sufficient conditions, in terms of forbidden...
Zsolt Tuza (2013)
Discussiones Mathematicae Graph Theory
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Given a graph G = (V,E) and a set Lv of admissible colors for each vertex v ∈ V (termed the list at v), a list coloring of G is a (proper) vertex coloring ϕ : V → S v2V Lv such that ϕ(v) ∈ Lv for all v ∈ V and ϕ(u) 6= ϕ(v) for all uv ∈ E. If such a ϕ exists, G is said to be list colorable. The choice number of G is the smallest natural number k for which G is list colorable whenever each list contains at least k colors. In this note we initiate the study of graphs in which the choice...
Ján Plesník (1975)
Matematický časopis
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E. Bampis, A. Giannakos, A. Karzanov, Y. Manoussakis, I. Milis (2000)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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Ivan Gutman (1991)
Publications de l'Institut Mathématique
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Mihály Bakonyi, Aaron Bono (1997)
Czechoslovak Mathematical Journal
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The question of generalizing results involving chordal graphs to similar concepts for chordal bipartite graphs is addressed. First, it is found that the removal of a bisimplicial edge from a chordal bipartite graph produces a chordal bipartite graph. As consequence, occurance of arithmetic zeros will not terminate perfect Gaussian elimination on sparse matrices having associated a chordal bipartite graph. Next, a property concerning minimal edge separators is presented. Finally, it is...