In this article, we relate the spectrum of discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties graph: existence perfect matching and Hamiltonian cycle underlying graph. particular, give family spectral obstructions parametrised by potential for to be matchable (i.e., having matching) or cycle. We base our analysis special case preorder introduced in [8], us...

In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a matching dimension to the game. This game is played on a graph $G$ by two players, named Dominator and Pairer. They alternately take turns choosing vertices of $G$ such that each vertex chosen by Domin...

An induced matching M of a graph G is a set of pairwise non-adjacent edges such that their end-vertices induce a 1-regular subgraph. An induced matching M is maximal if no other induced matching contains M . The MINIMUM MAXIMAL INDUCED MATCHING problem asks for a minimum maximal induced matching in a given graph. The problem is known to be NP-complete. Here we show that, if P 6= NP, for any ε >...

In this paper, we study the parameterized complexity and inapproximability of the Induced Matching problem in hamiltonian bipartite graphs. We show that, given a hamiltonian cycle in a hamiltonian bipartite graph, the problem is W[1]-hard and cannot be solved in time n 1 2 ) unless W[1]=FPT, where n is the number of vertices in the graph. In addition, we show that unless NP=P, the maximum induc...

It is well known that a stable matching in a two-sided matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a stable matching with high probability. In particular we allow the number of couples grow in an ‘almost’ linear rate. Furthermore, the mechanism induced by the...

The matching preclusion number of an even graph 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. Recently, the conditional matching preclusion number of an even graph was introduced to look for obstruction sets beyond those induced by a single vertex...