A (homogeneous) d-interval is a union of d closed intervals in the line. Using topological methods, Tardos and Kaiser proved that for any finite collection of d-intervals that contains no k + 1 pairwise disjoint members, there is a set of O(dk) points that intersects each member of the collection. Here we give a short, elementary proof of this result. A (homogeneous) d-interval is a union of d ...

The problem of finding a perfect matching in an arbitrary simple graph is well known and popular theory. It used various fields, such as chemistry, combinatorics, game theory etc. M G set pairwise nonadjacent edges, ie, those that do not have common vertices. Matching called if it covers all vertices the graph, ie each incidental to exactly one edges. By Koenig's theorem, regular bipartite grap...

We present an extension of the ( )-calculus with a case construct that propagates through functions like a head linear substitution, and show that this construction permits to recover the expressiveness of ML-style pattern matching. We then prove that this system enjoys the Church-Rosser property using a semi-automatic `divide and conquer' technique by which we determine all the pairs of commut...

This paper discusses the problem of trying to distinguish multicoloured objects which share similar colours. It introduces the Colour Region Adjacency Graph which describes the arrangement of colours on an object's surface followed by an graph matching procedure to recog-nise like and unlike objects. The paper also shows how the CRAG representation can be used to locate a model in a test image.

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...

Let [n]r be the complete r-partite hypergraph with vertex classes of size n. It is an easy exercise to show that every set of more than (k − 1)nr−1 edges in [n]r contains a matching of size k. We conjecture the following rainbow version of this observation: If F1, F2, . . . , Fk ⊆ [n]r are of size larger than (k− 1)nr−1 then there exists a rainbow matching, i.e. a choice of disjoint edges fi ∈ ...

A palindrome is a string that reads the same forward and backward. We say that two strings of the same length are pal-equivalent if for each possible center they have the same length of the maximal palindrome. Given a text T of length n and a set of patterns P1, . . . , Pk, we study the online multiple palindrome pattern matching problem that finds all pairs of an index i and a pattern Pj such ...

Let KN denote the complete k-graph on N vertices, that is, the k-uniform hypergraph whose edges are the (k) k-subsets of a set of N vertices . The Ramsey number of a pair of k-graphs is defined as for graphs in terms of the 2-colorings of the k-sets which are the edges of a complete k-graph . Let sKk denote a k-graph which is a matching with s edges . That is, sKk has sk vertices and s edges, n...

We consider how to index strings, trees and graphs for jumbled pattern matching when we are asked to return a match if one exists. For example, we show how, given a tree containing two colours, we can build a quadratic-space index with which we can find a match in time proportional to the size of the match. We also show how we need only linear space if we are content with approximate matches.

Let H = (V,E) be an r-uniform hypergraph and let F ⊂ 2 . A matching M of H is (α,F)perfect if for each F ∈ F , at least α|F | vertices of F are covered by M . Our main result is a theorem giving sufficient conditions for an r-uniform hypergraph to have a (1− ,F)-perfect matching. As a special case of our theorem we obtain the following result. Let K(n, r) denote the complete r-uniform hypergrap...