arXiv subjects
Publications and source records attributed to V. V. Mkrtchyan.
The paper presents a course on Combinatorial Algorithms that is based on the drafts of the author that he used while teaching the course in the Department of Informatics and Applied Mathematics of Yerevan State University, Armenia from February 2007 to June 2007.
For a graph consider the pairs of disjoint matchings which union contains as many edges as possible, and define a parameter $α$ which eqauls the cardinality of the largest matching in those pairs. Also, define $\betta$ to be the cardinality of a maximum matching of the graph. We give a constructive characterization of trees which satisfy the $α$=$\betta$ equality. The proof of our main theorem is based on a new decomposition algorithm obtained for trees.
For a graph G, consider the pairs of edge-disjoint matchings whose union consists of as many edges as possible. Let H be the largest matching among such pairs. Let M be a maximum matching of G. We show that 5/4 is a tight upper bound for |M|/|H|.
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding polynomial algorithms.
For bipartite graphs the NP-completeness is proved for the problem of existence of maximum matching which removal leads to a graph with given lower(upper)bound for the cardinality of its maximum matching.
A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.
I prove that in a tree in which the distance between any two endpoints is even, there is a maximum proper partial 0-1 coloring such that the edges colored by 0 form a maximum matching.