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Let d and t be fixed positive integers, and let denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem ...
A classic result of Erdos, Gyarfas and Pyber states that for every coloring of the edges of K-n with r colors, there is a cover of its vertex set by at most f(r)=O(r2logr) vertex-disjoint monochromatic cycles. In particular, the minimum number of such cove ...
We consider a set V of elements and an optimization problem on V: the search for a maximum (or minimum) cardinality subset of V verifying a given property a"similar to. A d-transversal is a subset of V which intersects any optimum solution in at least d el ...
We prove that every 3-coloring of the edges of the complete graph on n vertices without a rainbow triangle contains a set of order ohm(n(1/3) log(2) n) which uses at most two colors, and this bound is tight up to a constant factor. This verifies a conjectu ...
The generation of synthetic populations through simulation methods is an important research topic and has a key application in agent-based modeling of transport and land use. The next step in this research area is the generation of complete synthetic house ...
We present an efficient matching method for generalized geometric graphs. Such graphs consist of vertices in space connected by curves and can represent many real world structures such as road networks in remote sensing, or vessel networks in medical imagi ...
Graph matching is a generalization of the classic graph isomorphism problem. By using only their structures a graph-matching algorithm finds a map between the vertex sets of two similar graphs. This has applications in the de-anonymization of social and in ...
We present an O(m^10/7) = O(m^1.43)-time algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities. This is the first improvement over the sparse-graph case of the long-standing O(m min{m^1/2, n^2/3}) runni ...
Let G=(V,E)G=(V,E) be a graph in which every vertex v∈Vv∈V has a weight w(v)⩾0w(v)⩾0 and a cost c(v)⩾0c(v)⩾0. Let SGSG be the family of all maximum-weight stable sets in G . For any integer d⩾0d⩾0, a minimum d-transversal in the graph G with respect to SGS ...