In Image Database Systems, symbolic pictures are represented by 2D strings that are converted into triples. Each triple is mapped to a unique hash address for timely retrieval of pictures, reducing the pattern-matching problem corresponding to a query to that of computation of hash function. The values associated with the picture objects are used to compute hash addresses for triples developed ...

A graph G having a perfect matching (or I-factor) is called n-fextendable if every matching of size n is extended to a I-factor. Further, G is said to be (r : m, n }-extendable if, for every connected subgraph S of order 2r for which G \ V(S) is connected, S is m-extendable and G \ V(S) is nextendable. We prove the following: Let p, r, m, and n be positive integers with p r > nand r > m. Then e...

The resonance graph R(B) of a benzenoid graph B has the perfect matchings of B as vertices, two perfect matchings being adjacent if their symmetric difference forms the edge set of a hexagon of B . A family P of pair-wise disjoint hexagons of a benzenoid graph B is resonant in B if B−P contains at least one perfect matching, or if B − P is empty. It is proven that there exists a surjective map ...

Perfect matchings and series-parallel graphs: multiplicatives proof nets as R&B-graphs Extended Abstract] Abstract A graph-theoretical look at multiplicative proof nets lead us to two new descriptions of a proof net, both as a graph endowed with a perfect matching. The rst one is a rather conventional encoding of the connectives which nevertheless allows us to unify various sequentialisation te...

We call a graph matching-covered if every line belongs to a perfect matching. We study the technique of "ear-decompositions" of such graphs. We prove that a non-bipartite matchingcovered graph contains K~ or K2@Ka (the triangular prism). Using this result, we give new characterizations of those graphs whose matching and covering numbers are equal. We apply these results to the theory of r-criti...

Let R and B be sets of n red and n blue points in the plane, respectively, with P = R∪ B. Let M be a perfect matching between points from R and B, using n straight line segments to match the points, that is, each point is an endpoint of exactly one line segment, and each line segment has one red and one blue endpoint. We forbid line segments to cross. Denote the length of a longest line segment...

The perfect matching complex of a graph is the simplicial on edge set with facets corresponding to matchings graph. This paper studies complexes, $\mathcal{M}_p(H_{k \times m\times n})$, honeycomb graphs. For $k = 1$, $\mathcal{M}_p(H_{1\times n})$ contractible unless $n\geq m=2$, in which case it homotopy equivalent $(n-1)$-sphere. Also, $\mathcal{M}_p(H_{2\times 2\times 2})$ wedge two 3-spher...