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Signed b-matchings and b-edge covers of strong product graphs

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In this paper, we study the signed b-edge cover number and the signed b-matching number of a graph. Sharp bounds on these parameters of the strong product graphs are presented. We prove the existence of an analogue of Gallai's theorem relating maximum-size signed b-matchings and minimum-size signed b-edge covers for the complete graphs and complete bipartite graphs.


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