A perfect matching in a graph G is set of nonadjacent edges covering every vertex G. Motivated by recent progress on the relations between eigenvalues and number graph, this paper, we aim to present distance spectral radius condition guarantee existence matching. Let be an n-vertex connected where n even λ1(D(G)) Then following statements are true. (I) If 4≤n≤8 λ1(DG)≤λ1(D(Sn,n2−1)), then conta...

The bipartite matching problem has wide applicability. For example, in computer science, researchers have applied bipartite matching in objection recognition, image processing, scheduling, genomics, term rewriting and formal verification, and computer security. We present a heuristic model of perfect matchings in bipartite graphs. The goal of the model is to explore the use of low-cost heuristi...

Abstract The well-known -complete problem Matching Cut is to decide if a graph has matching that also an edge cut of the graph. We prove new complexity results for restricted H -free graphs, is, graphs do not contain some fixed as induced subgraph. two recently studied variants , on graphs. first variant requires must be extendable perfect second matching. In particular, we there exists small c...

A 2-matching in an undirected graph G = (V G,EG) is a function x : EG → {0, 1, 2} such that for each node v ∈ V G the sum of values x(e) on all edges e incident to v does not exceed 2. The size of x is the sum ∑ e x(e). If {e ∈ EG | x(e) 6= 0} contains no triangles then x is called triangle-free. Cornuéjols and Pulleyblank devised a combinatorial O(mn)-algorithm that finds a triangle free 2-mat...

In this paper, we consider the problem of finding an edge coloring of a d-regular bipartite multigraph with 2n vertices and m = nd edges. The best known deterministic algorithm (by Cole, Ost, and Schirra) takes O(m log d) time to find an edge coloring of such a graph. This bound is achieved by combining an O(m)-time perfect-matching algorithm with the Euler partition algorithm. The O(m) time bo...

Let G = (V, E) be an (edge-)colored graph, i.e., G is assigned a mapping C : E → {1, 2, · · · , r}, the set of colors. A matching of G is called heterochromatic if its any two edges have different colors. Unlike uncolored matchings for which the maximum matching problem is solvable in polynomial time, the maximum heterochromatic matching problem is NP-complete. This means that to find both suff...