The fractional matching preclusion number of complete n-balanced k-partite graphs

Yu Luan (), Mei Lu () and Yi Zhang ()
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Yu Luan: Tsinghua University
Mei Lu: Tsinghua University
Yi Zhang: Beijing University of Posts and Telecommunications

Journal of Combinatorial Optimization, 2022, vol. 44, issue 2, No 20, 1323-1329

Abstract: Abstract The fractional matching preclusion number of a graph G, denoted by fmp(G), is the minimum number of edges whose deletion results in a graph with no fractional perfect matchings. Let $$G_{k,n}$$ G k , n be the complete n-balanced k-partite graph, whose vertex set can be partitioned into k parts, each has n vertices and whose edge set contains all edges between two distinct parts. In this paper, we prove that if $$k=3$$ k = 3 or 5 and $$n=1$$ n = 1 , then $$fmp(G_{k,n})=\delta (G_{k,n})-1$$ f m p ( G k , n ) = δ ( G k , n ) - 1 ; otherwise $$fmp(G_{k,n})=\delta (G_{k,n})$$ f m p ( G k , n ) = δ ( G k , n ) .

Keywords: Fractional matching preclusion number; n-balanced k-partite graph; Fractional perfect matching (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-022-00888-5

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