The Pfaffian property of Cartesian products of graphs

Fuliang Lu and Lianzhu Zhang ()
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Fuliang Lu: Linyi University
Lianzhu Zhang: Xiamen University

Journal of Combinatorial Optimization, 2014, vol. 27, issue 3, No 8, 530-540

Abstract: Abstract Suppose that G=(V,E) is a graph with even vertices. An even cycle C is a nice cycle of G if G−V(C) has a perfect matching. An orientation of G is a Pfaffian orientation if each nice cycle C has an odd number of edges directed in either direction of the cycle. Let P n and C n denote the path and the cycle on n vertices, respectively. In this paper, we characterize the Pfaffian property of Cartesian products G×P 2n and G×C 2n for any graph G in terms of forbidden subgraphs of G. This extends the results in (Yan and Zhang in Discrete Appl Math 154:145–157, 2006).

Keywords: Perfect matchings; Pfaffian graphs; Cartesian products of graphs (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-012-9533-4

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