Let G be an edge-coloured graph. A rainbow subgraph in G is a subgraph such that its edges have distinct colours. The minimum colour degree δc(G) of G is the smallest number of distinct colours on the edges incidentwith a vertex ofG.We show that every edge-coloured graph G on n ≥ 7k/2 + 2 vertices with δc(G) ≥ k contains a rainbow matching of size at least k, which improves the previous result ...

The authors regret that Table 2 contains an error in the original article, the correct table appears below. The authors would like to apologise for any inconvenience caused.

Real Scaled Matching is the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary real-sized scale, appears. Real scaled matching is an important problem that was originally inspired by Computer Vision. In this paper, we present a new, more precise and realistic, definition for one dimensional real scaled matching, and an efficient alg...

We give a characterization of matchings in terms of the canonical reduced decompositions. As an application, the canonical reduced decompositions of 12312avoiding matchings are obtained. Based on such decompositions, we find a bijection between 12312-avoiding matchings and ternary paths.

A graph G with at least 2m + 2 edges is said to be distance d m-extendable if for any matching M in G with m edges in which the edges lie pair-wise distance at least d, there exists a perfect matching in G containing M . In a previous paper, Aldred and Plummer proved that every 5-connected triangulation of the plane or the projective plane of even order is distance 5 m-extendable for any m. In ...

Let Gm,σ be the collection of all weighted bipartite graphs each having σ and m, as the size of a vertex partition and the total weight, respectively. We give a tight lower bound dm−σ σ e+ 1 for the set {Wt(mwm(G)) | G ∈ Gm,σ} which denotes the collection of weights of maximum weight bipartite matchings of all graphs in Gm,σ.

We study the i.i.d. online bipartite matching problem, a dynamic version of the classical model where one side of the bipartition is fixed and known in advance, while nodes from the other side appear one at a time as i.i.d. realizations of a uniform distribution, and must immediately be matched or discarded. We consider various relaxations of the polyhedral set of achievable matching probabilit...

For a graph G, consider the pairs of edge-disjoint matchings whose union consists of as many edges as possible. Let H be the largest matching among such pairs. Let M be a maximum matching of G. We show that 5/4 is a tight upper bound for |M |/|H |.

Many methods of graphics recognition have been developed throughout the years for the recognition of pre-segmented graphics symbols but very few techniques achieved the objective of symbol spotting and recognition together in a generic case. To go one step forward through this objective, this paper presents an original solution for symbol spotting using a graph representation of graphical docum...

We study flag enumeration in intervals in the uncrossing partial order on matchings. We produce a recursion for the cd-indices of intervals in the uncrossing poset Pn. We explicitly describe the matchings by constructing an order-reversing bijection. We obtain a recursion for the ab-indices of intervals in the poset P̂n, the poset Pn with a unique minimum 0̂ adjoined.