Let the matching polynomial of a graph G be denoted by μ(G, x). A graph G is said to be θ-super positive if μ(G, θ) 6= 0 and μ(G \ v, θ) = 0 for all v ∈ V (G). In particular, G is 0-super positive if and only if G has a perfect matching. While much is known about 0-super positive graphs, almost nothing is known about θsuper positive graphs for θ 6= 0. This motivates us to investigate the struct...

Given a graphG = (V,E) and for each vertex v ∈ V a subsetB(v) of the set {0, 1, . . . , dG(v)}, where dG(v) denotes the degree of vertex v in the graph G, a B-matching of G is any set F ⊆ E such that dF (v) ∈ B(v) for each vertex v, where dF (v) denotes the number of edges of F incident to v. The general matching problem asks the existence of aB-matching in a given graph. A setB(v) is said to h...

Graph pattern matching is among the most costly operations in any graph transformation system. Incremental pattern matching aims at reducing this cost by incrementally updating, as opposed to totally recalculating, the possible matches of rules in the graph grammar at each step of the transformation. In this paper an implementation of one such algorithm is discussed with respect to the GROOVE t...

Let n be a positive integer with n $; (V(O)-2)/2. A graph G is nextendable if it contains a set of n independent edges and every set of n independent edges can be extended to a perfect matching of G. In this paper, we give a characterization of n-extendable graphs. The characterizations of other matching extension are also discussed.

Let n be a non-negative integer. A graph G is said to be n-matchable if the subgraph G − S has a perfect matching for any subset S of V (G) with |S| = n. In this paper, we obtain sufficient conditions for different classes of graphs to be n-matchable. Since 2k-matchable graphs must be k-extendable, we have generalized the results about k-extendable graphs. All results in this paper are sharp.

This article deals with the problem of classification of human activities from video. Our approach uses motion features that are computed very efficiently, and subsequently projected into a lower dimensional space where matching is performed. Each action is represented as a manifold in this lower dimensional space and matching is done by comparing these manifolds. To demonstrate the effectivene...

The structural theory of matchings is used to establish lower bounds on the number of perfect matchings in n-extendable graphs. It is shown that any such graph on p vertices and q edges contains at least (n + 1)!/4[q − p − (n − 1)(2 − 3) + 4] different perfect matchings, where is the maximum degree of a vertex in G. © 2007 Elsevier B.V. All rights reserved. MSC: 05C70; 05C40; 05C75

We define and consider k-distant crossings and nestings for matchings and set partitions, which are a variation of crossings and nestings in which the distance between vertices is important. By modifying an involution of Kasraoui and Zeng (Electronic J. Combinatorics 2006, research paper 33), we show that the joint distribution of k-distant crossings and nestings is symmetric. We also study the...