3 research outputs found
Finding a Maximum Restricted -Matching via Boolean Edge-CSP
The problem of finding a maximum -matching without short cycles has
received significant attention due to its relevance to the Hamilton cycle
problem. This problem is generalized to finding a maximum -matching which
excludes specified complete -partite subgraphs, where is a fixed
positive integer. The polynomial solvability of this generalized problem
remains an open question. In this paper, we present polynomial-time algorithms
for the following two cases of this problem: in the first case the forbidden
complete -partite subgraphs are edge-disjoint; and in the second case the
maximum degree of the input graph is at most . Our result for the first
case extends the previous work of Nam (1994) showing the polynomial solvability
of the problem of finding a maximum -matching without cycles of length four,
where the cycles of length four are vertex-disjoint. The second result expands
upon the works of B\'{e}rczi and V\'{e}gh (2010) and Kobayashi and Yin (2012),
which focused on graphs with maximum degree at most . Our algorithms are
obtained from exploiting the discrete structure of restricted -matchings and
employing an algorithm for the Boolean edge-CSP.Comment: 20 pages, 2 figure