Matching Preclusion Research Articles

Matching preclusion and conditional matching preclusion for bipartite interconnection networks II: Cayley graphs generated by transposition trees and hyper‐stars

AbstractThe matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. It is natural to look for obstruction sets beyond those induced by a single vertex. The conditional matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph with no isolated vertices that has no perfect matchings. In this companion paper of Cheng et al. (Networks (NET 1554)), we find these numbers for a number of popular interconnection networks including hypercubes, star graphs, Cayley graphs generated by transposition trees and hyper‐stars. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011

Matching preclusion and conditional matching preclusion for bipartite interconnection networks I: Sufficient conditions

AbstractThe matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost‐perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. This number is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost‐perfect matchings. In this article, we prove general results regarding the matching preclusion number and the conditional matching preclusion number as well as the classification of their respective optimal sets for bipartite graphs. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011

Conditional matching preclusion for the alternating group graphs and split-stars

The matching preclusion number of a graph is the minimum number of edges the deletion of which results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges the deletion of which results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In this article, we find this number and classify all optimal sets for the alternating group graphs, one of the most popular interconnection networks, and their companion graphs, the split-stars. Moreover, some general results on the conditional matching preclusion problems are also presented.

Matching preclusion for the (n, k)-bubble-sort graphs

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. In this paper, we find this number for the (n, k)-bubble-sort graphs and classify all the optimal solutions.

Matching preclusion for [formula omitted]-ary [formula omitted]-cubes

The (conditional) matching preclusion number of a graph is the minimum number of edges whose deletion leaves a resulting graph (with no isolated vertices) that has neither perfect matchings nor almost perfect matchings. In this paper, we prove that the matching preclusion number and the conditional matching preclusion number of the k -ary n -cube with even k ≥ 4 are 2 n and 4 n − 2 , respectively.

MATCHING PRECLUSION AND CONDITIONAL MATCHING PRECLUSION FOR AUGMENTED CUBES

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those incident to a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those incident to a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In this paper, we find this number and classify all optimal sets for the augmented cubes, a class of networks designed as an improvement of the hypercubes.

Conditional matching preclusion for hypercube-like interconnection networks

The conditional matching preclusion number of a graph with n vertices is the minimum number of edges whose deletion results in a graph without an isolated vertex that does not have a perfect matching if n is even, or an almost perfect matching if n is odd. We develop some general properties on conditional matching preclusion and then analyze the conditional matching preclusion numbers for some HL-graphs, hypercube-like interconnection networks.

MATCHING PRECLUSION FOR ALTERNATING GROUP GRAPHS AND THEIR GENERALIZATIONS

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. In this paper, we find this number for the alternating group graphs, Cayley graphs generated by 2-trees and the (n,k)-arrangement graphs. Moreover, we classify all the optimal solutions.

Conditional matching preclusion sets

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. In this paper, we look for obstruction sets beyond these sets. We introduce the conditional matching preclusion number of a graph. It is the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. We find this number and classify all optimal sets for several basic classes of graphs.

Matching preclusion for some interconnection networks

AbstractThe matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost‐perfect matchings. In this paper, we find this number for various classes of interconnection networks and classify all the optimal solutions. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(2), 173–180 2007