The signed matchings in graphs
Changping Wang
Discussiones Mathematicae Graph Theory, Tome 28 (2008), p. 477-486 / Harvested from The Polish Digital Mathematics Library
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Let G be a graph with vertex set V(G) and edge set E(G). A signed matching is a function x: E(G) → -1,1 satisfying ∑e∈EG(v)x(e)≤1 for every v ∈ V(G), where EG(v)=uv∈E(G)|u∈V(G). The maximum of the values of ∑e∈E(G)x(e), taken over all signed matchings x, is called the signed matching number and is denoted by β’₁(G). In this paper, we study the complexity of the maximum signed matching problem. We show that a maximum signed matching can be found in strongly polynomial-time. We present sharp upper and lower bounds on β’₁(G) for general graphs. We investigate the sum of maximum size of signed matchings and minimum size of signed 1-edge covers. We disprove the existence of an analogue of Gallai’s theorem. Exact values of β’₁(G) of several classes of graphs are found.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:270160 
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Changping Wang. The signed matchings in graphs. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 477-486. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1421/

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