MATCHING PROBLEMS WITH DELTA-MATROID CONSTRAINTS

作者：Kakimura Naonori^*; Takamatsu Mizuyo

来源：SIAM Journal on Discrete Mathematics, 2014, 28(2): 942-961.

DOI：10.1137/110860070

• constrained matching
• delta-matroid
• polynomial-time algorithm
• mixed matrix theory

Given an undirected graph G = (V, E) and a delta-matroid (V, F), the delta-matroid matching problem is to find a maximum cardinality matching M such that the set of the end vertices of M belongs to F. This problem is a natural generalization of the matroid matching problem to delta-matroids, and thus it cannot be solved in polynomial time in general. This paper introduces a class of the delta-matroid matching problem, where the given delta-matroid is a projection of a linear delta-matroid. We first show that it can be solved in polynomial time if the given linear delta-matroid is generic. This result enlarges a polynomially solvable class of matching problems with precedence constraints on vertices such as the 2-master/slave matching. In addition, we design a polynomial-time algorithm when the graph is bipartite and the delta-matroid is defined on one vertex side. This result is extended to the case where a linear matroid constraint is additionally imposed on the other vertex side.

• 出版日期2014