Anti-forcing spectra of perfect matchings of graphs

Kai Deng () and Heping Zhang ()
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Kai Deng: Lanzhou University
Heping Zhang: Lanzhou University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 2, No 18, 660-680

Abstract: Abstract Let M be a perfect matching of a graph G. The smallest number of edges whose removal to make M as the unique perfect matching in the resulting subgraph is called the anti-forcing number of M. The anti-forcing spectrum of G is the set of anti-forcing numbers of all perfect matchings in G, denoted by $$\hbox {Spec}_{af}(G)$$ Spec a f ( G ) . In this paper, we show that any finite set of positive integers can be the anti-forcing spectrum of a graph. We present two classes of hexagonal systems whose anti-forcing spectra are integer intervals. Finally, we show that determining the anti-forcing number of a perfect matching of a bipartite graph with maximum degree four is a NP-complete problem.

Keywords: Perfect matching; Anti-forcing number; Anti-forcing spectrum; Hexagonal system (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-015-9986-3

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