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arXiv · 0901.0121

On upper bounds for parameters related to construction of special maximum matchings

Artur Khojabaghyan·Vahan V. Mkrtchyan
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Abstract

For a graph $G$ let $L(G)$ and $l(G)$ denote the size of the largest and smallest maximum matching of a graph obtained from $G$ by removing a maximum matching of $G$. We show that $L(G)\leq 2l(G),$ and $L(G)\leq (3/2)l(G)$ provided that $G$ contains a perfect matching. We also characterize the class of graphs for which $L(G)=2l(G)$. Our characterization implies the existence of a polynomial algorithm for testing the property $L(G)=2l(G)$. Finally we show that it is $NP$-complete to test whether a graph $G$ containing a perfect matching satisfies $L(G)=(3/2)l(G)$.

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Artur Khojabaghyan, Vahan V. Mkrtchyan. 2011-07-25. On upper bounds for parameters related to construction of special maximum matchings. https://doi.org/10.1016/j.disc.2011.08.026

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