Abstract
A signed k-submatching of a graph G is a function f : E(G) → {−1,1} satisfying f (E G (v)) ≤ 1 for at least k vertices \({v \in V(G)}\). The maximum of the values of f (E(G)), taken over all signed k-submatchings f, is called the signed k-submatching number and is denoted by \({\beta_S^{k}(G)}\). In this paper, sharp bounds on \({\beta_S^{k}(G)}\) for general graphs are presented. Exact values of \({\beta_S^{k}(G)}\) for several classes of graphs are found.
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References
Chartrand G., Lesniak L.: Graphs & Digraphs, 3rd edn. Chapman and Hall, Boca Raton (2000)
Schrijver A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin (2004)
Wang C.: The signed matchings in graphs. Discuss. Math. Graph Theory 28, 477–486 (2008)
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Wang, C. The Signed k-Submatchings in Graphs. Graphs and Combinatorics 29, 1961–1971 (2013). https://doi.org/10.1007/s00373-012-1222-7
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DOI: https://doi.org/10.1007/s00373-012-1222-7