Braces of Perfect Matching Width 2

by   Archontia C. Giannopoulou, et al.

A graph G is called matching covered if it is connected and every edge is contained in a perfect matching. Perfect matching width is a width parameter for matching covered graphs based on a branch decomposition that can be considered a generalisation of directed treewidth. We show that the perfect matching width of every bipartite matching covered graph is within a factor of 2 of the perfect matching width of its braces. Moreover, we give characterisations for braces of perfect matching width in terms of edge maximal graphs similar to k-trees for undirected treewidth and elimination orderings. The latter allows us to identify braces of perfect matching width 2 in polynomial time and provides an algorithm to construct an optimal decomposition.



There are no comments yet.



Cyclewidth and the Grid Theorem for Perfect Matching Width of Bipartite Graphs

A connected graph G is called matching covered if every edge of G is con...

How many matchings cover the nodes of a graph?

Given an undirected graph, are there k matchings whose union covers all ...

A Complete Anytime Algorithm for Treewidth

In this paper, we present a Branch and Bound algorithm called QuickBB fo...

Two Disjoint Alternating Paths in Bipartite Graphs

A bipartite graph B is called a brace if it is connected and every match...

Bipartite Perfect Matching as a Real Polynomial

We obtain a description of the Bipartite Perfect Matching decision probl...

Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

Motivated by adjacency in perfect matching polytopes, we study the short...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.