In this paper we consider properly edge-colored graphs, i.e. two edges with the same color cannot share an endpoint, so each color class is a matching. A matching is called rainbow if its edges have different colors. The minimum degree of a graph is denoted by δ(G). We show that properly edge colored graphs G with |V (G)| ≥ 4δ(G) − 3 have rainbow matchings of size δ(G), this gives the best know...

In the process of high resolution images orthorectification, an uneven distribution of ground control points in mountainous area results in the phenomenon of ground objects dislocation between orthophotos edges in the overlap area. Followed image mosaic, fusion and interpretation are seriously affected. High-resolution (2.5 m) panchromatic images with a 30% forward overlap of ALOS satellite wer...

In this paper, we propose a robust method to register a panoramic range data obtained by a panoramic laser range finder and an omni-directional image acquired by a stereo omni-directional system (SOS), by matching the horizontal and vertical edge histograms of the two images. The proposed method first estimates the relative horizontal rotation angle by matching the vertical edge histograms. Nex...

For any graph H, let Forb∗(H) be the class of graphs with no induced subdivision of H. It was conjectured in [A.D. Scott, Induced trees in graphs of large chromatic number, Journal of Graph Theory, 24:297– 311, 1997] that, for every graph H, there is a function fH : N → R such that for every graph G ∈ Forb∗(H), χ(G) ≤ fH(ω(G)). We prove this conjecture for several graphs H, namely the paw (a tr...

The goal of this paper is to find a competitive algorithm for the following problem. We are given a hypergraph G = (X,E), |E| = n, with weighted edges and maximum edge size k. We wish to maximize the weight of a matching M ⊆ E of G, given that edges are revealed in a random order, and that when an edge e is revealed the algorithm must decide either e ∈ M or e / ∈M . Note that this is a generali...

Given a positive integer n we find a graph G = (V,E) on |V | = n vertices with a minimum number of edges such that for any pair of non adjacent vertices x, y the graph G − x − y contains a (almost) perfect matching M . Intuitively the non edge xy and M form a (almost) perfect matching of G. Similarly we determine a graph G = (V,E) with a minimum number of edges such that for any matching M̄ of t...

Let G = (V,E) be an edge-colored graph, i.e., G is assigned a surjective function C : E → {1, 2, · · · , r}, the set of colors. A matching of G is called heterochromatic if its any two edges have different colors. Let (B,C) be an edge-colored bipartite graph and d(v) be color degree of a vertex v. We show that if d(v) ≥ k for every vertex v of B, then B has a heterochromatic matching of cardina...

ÐImage matching applications such as tracking and stereo commonly use the sum-of-squared-difference (SSD) measure to determine the best match. However, this measure is sensitive to outliers and is not robust to template variations. Alternative measures have also been proposed that are more robust to these issues. We improve upon these using a probabilistic formulation for image matching in term...