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The signed matchings in graphs

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Wang C.

Discussiones Mathematicae Graph Theory

2008

tom 28

nr 3

477-486

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 $∑_{e ∈ E_G(v)} x(e) ≤ 1$ for every v ∈ V(G), where $E_G(v) = {uv ∈ E(G)| u ∈ V(G)}$. 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.

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1 Discussiones Mathematicae Graph Theory

1 Wang C.

1 2008

Wyniki wyszukiwania

The signed matchings in graphs