Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E′ ⊆ E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E′ then E′ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to de...

Eroh and Oellerman defined BRR(G1, G2) as the smallest N such that any edge coloring of the complete bipartite graph KN,N contains either a monochromatic G1 or a multicolored G2. We restate the problem of determining BRR(K1,λ,Kr,s) in matrix form and prove estimates and exact values for several choices of the parameters. Our general bound uses Füredi’s result on fractional matchings of uniform ...

Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E′ ⊆ E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E′ then E′ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to de...

In this paper, we proposed a temporal error concealment (EC) using the concealed boundary pixels and the adaptive block matching method. The proposed boundary matching method improves the spatial correlation of the macroblocks (MBs) by reusing the pixels of the concealed MB to estimate a motion vector of a error MB. The adaptive block matching method inspects horizontal edge and vertical edge f...

In an n by n complete bipartite graph with independent exponentially distributed edge costs, we ask for the minimum total cost of a set of edges of which each vertex is incident to at least one. This so-called minimum edge cover problem is a relaxation of perfect matching. We show that the large n limit cost of the minimum edge cover is W (1)2 + 2W (1) ≈ 1.456, where W is the Lambert W -functio...

We define a problem called Simplex Matching and show that it is solvable in polynomial time. While Simplex Matching is interesting in its own right as a nontrivial extension of nonbipartite min-cost matching, its main value lies in many (seemingly very different) problems that can be solved using our algorithm. For example, suppose that we are given a graph with terminal nodes, nonterminal node...

A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.

In this paper we deal with simple finite undirected graphs (no loops and no multiple edges). G = (V, E) denotes a graph with vertex set V and edge set E. A matching of a graph is a set of nonadjacent edges, and a maximum matching, denoted by M(G), of G is one of maximum cardinality. n(G) denotes the number of unsaturated vertices (i.e., vertices with which no edge of a matching is incident) in ...