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10 papers · 1 filter
Lower bounds on the obstacle number of graphs
Padmini Mukkamala, János Pach, Dömötör Pálvölgyi
Given a graph , an {\em obstacle representation} of is a set of points in the plane representing the vertices of , together with a set of connected obstacles such that tw…
Characterizing partition functions of the vertex model
Jan Draisma, Dion Gijswijt, László Lovász +2
We characterize which graph parameters are partition functions of a vertex model over an algebraically closed field of characteristic 0 (in the sense of de la Harpe and Jones). We…
Imbalances in directed multigraphs
S. Pirzada, T. A. Naikoo, U. Samee +1
In a directed multigraph, the imbalance of a vertex is defined as , where and denote the outdegree an…
Reconstruction of complete interval tournaments. II
Antal Iványi
Let and be nonnegative integers and let be the set of such generalised tournaments, in which every pair of distinct play…
Left and right convergence of graphs with bounded degree
Christian Borgs, Jennifer Chayes, Jeff Kahn +1
The theory of convergent graph sequences has been worked out in two extreme cases, dense graphs and bounded degree graphs. One can define convergence in terms of counting homomorph…
Borel oracles. An analytical approach to constant-time algorithms
Gabor Elek, Gabor Lippner
Nguyen and Onak constructed the first constant-time algorithm for the approximation of the size of the maximum matching in bounded degree graphs. The Borel oracle machinery is a to…