Let M, N be two matchings on [2n] (possibly M = N) and for an integer l ≥ 0 let T (M, l) be the set of those matchings on [2n + 2l] which can be obtained from M by successively adding l times in all ways the first edge, and similarly for T (N, l). Let s, t ∈ {cr, ne} where cr is the statistic of the number of crossings (in a matching) and ne is the statistic of the number of nestings (possibly ...

We consider, for complete bipartite graphs, the convex hulls of characteristic vectors of matchings, extended by a binary number indicating whether the matching contains two specific edges. This polytope is associated to the quadratic matching problem with a single linearized quadratic term. We provide a complete irredundant inequality description, which settles a conjecture by Klein (Ph.D. the...

For a given graph H and n¿ 1, let f(n; H) denote the maximum number m for which it is possible to colour the edges of the complete graph Kn with m colours in such a way that each subgraph H in Kn has at least two edges of the same colour. Equivalently, any edge-colouring of Kn with at least rb(n; H) = f(n; H) + 1 colours contains a rainbow copy of H . Erdős, Simonovits and S6 os have determined...

For any posotive integer m, let [m] := {1, . . . ,m}. Let n, k, t be positive integers. Aharoni and Howard conjectured that if, for i ∈ [t], Fi ⊂ [n] := {(a1, . . . , ak) : aj ∈ [n] for j ∈ [k]} and |Fi| > (t−1)n, then there exist M ⊆ [n] such that |M | = t and |M ∩ Fi| = 1 for i ∈ [t] We show that this conjecture holds when n ≥ 3(k − 1)(t− 1). Let n, t, k1 ≥ k2 ≥ . . . ≥ kt be positive integer...

A matching in a graph is a set of edges no two of which share a common vertex. A matching M is an induced matching if no edge connects two edges of M. The problem of finding a maximum induced matching is known to be NP-hard in general and specifically for bipartite graphs. Lozin has been proposed an O(n) time algorithm for this problem on the class of bipartite Star123, Sun4-free graphs. In thi...

A smart and simple algorithm is presented in this paper for vehicle’s license plate recognition system. Based on pattern matching, this algorithm can be applied for real time detection of license plates for collecting data for surveying or for some application specific purposes. The proposed system has been prototyped using C++ and the experimental results have been shown for recognition of Alb...