Let G be an (edge-)colored graph. A heterochromatic matching of G is a matching in which no two edges have the same color. For a vertex v, let d(v) be the color degree of v. We show that if d(v) ≥ k for every vertex v of G, then G has a heterochromatic matching of size ⌈ 5k−3 12 ⌉ . For a colored bipartite graph with bipartition (X,Y ), we prove that if it satisfies a Hall-like condition, then ...

For each b ≥ 5 we construct a pair of cospectral b-regular graphs, where one has a perfect matching and the other one not. This solves a research problem posed by the third author at the 22nd British Combinatorial Conference.

Summarizer is a system which helps in producing a condensed representation of its input ready for user consumption. Most important benefit of summary is to reduce size. This paper deals with importance of summarizers in our life. We describe various techniques such as graph matching, concept counting and hierarchy analysis etc. used by summarizer in producing summaries. Section III describes di...

We show that if G is a simple triangle-free graph with n ≥ 3 vertices, without a perfect matching, and having a minimum degree at least n−1 2 , then G is isomorphic either to C5 or to Kn−1 2 , n+1 2 .

Sketch-based retrieval is a technique that supports the design of behaviour for game characters by reusing previously designed behaviours. Most techniques for specifying behaviour for game characters use some kind of graph-based formalism to represent such behaviour. Through graph-matching techniques, sketch-based retrieval allows to use any intermediate graph generated along the design process...

Structure description and matching are useful techniques with wide area of applications. Common motivation could be the need for object identification. This work presents a specific method developed to describe and match particular type of structures – sets of points in two-dimensional space. The method incorporates creation of the structure description suitable for further matching and a proce...

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.

To investigate whether a persuasive game may serve as a way to increase attitude towards the homeless, this study examined the effects of persuasive mechanics in a video game designed to put the player in the shoes of an almost-homeless person. Data were collected from 5139 students in 200 middle/high school classes across four states. Classes were assigned to treatment groups based on matching...

In the present paper, the minimal proper alternating cycle (MPAC) rotation graph R(G) of perfect matchings of a plane bipartite graph G is defined. We show that an MPAC rotation graph R(G) of G is a directed rooted tree, and thus extend such a result for generalized polyhex graphs to arbitrary plane bipartite graphs. As an immediate result, we describe a one-to-one correspondence between MPAC s...

We will give a tight minimum co-degree condition for a 4-uniform hypergraph to contain a perfect matching.