In the online F-avoidance edge-coloring game with r colors, a graph on n vertices is generated by at each stage randomly adding a new edge. The player must color each new edge as ...
The r-parity tensor of a graph is a generalization of the adjacency matrix, where the tensor’s entries denote the parity of the number of edges in subgraphs induced by r distinc...
Abstract—The problem of hypothesis testing against independence for a Gauss–Markov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, an expression for the...
While it is exponentially unlikely that a sparse random graph or hypergraph is connected, with probability 1 − o(1) such a graph has a “giant component” that, given its numbe...
An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most one. The least positive integer k for which there exis...