Two mobile agents (robots) with distinct labels have to meet in an arbitrary, possibly infinite, unknown connected graph or in an unknown connected terrain in the plane. Agents ar...
In this short note we prove that there is a constant c such that every k-edge-coloring of the complete graph Kn with n 2ck contains a K4 whose edges receive at most two colors. Th...
For a directed graph G without loops or parallel edges, let (G) denote the size of the smallest feedback arc set, i.e., the smallest subset X E(G) such that G \ X has no directed...
We consider the problem of cheating in secret sharing schemes, cheating in which individuals submit forged shares in the secret reconstruction phase in an effort to make another pa...
We study here the spectra of random lifts of graphs. Let G be a finite connected graph, and let the infinite tree T be its universal cover space. If λ1 and ρ are the spectral ...