On Locally-Balanced 2-Partitions of Complete Multipartite Graphs - Aram H. Gharibyan; Petrosyan, Petros (Изд-во НАН РА)
A 2-partition of a graph G is a function f : V (G) ! fWhite;Blackg. A 2-partition f of a graph G is locally-balanced with an open neighborhood if for every v € V (G), ││{u € NG(v): f(u) =Whitegj}│-│{u € NG(v): f(u) = Black}││≤ 1, where NG(v) = fu 2 V (G): uv 2 E(G)g. A 2-partition f0 of a graph G is locallybalanced with a closed neighborhood if for every v € V(G), ││{u € NG[v]: f0(u) =White}│-│{u € NG[v] : f(u) = Black}││ ≤ 1, where NG[v] = NG(v) u [v}. In this paper we give necessary and su±cient conditions for the existence of locally-balanced 2-partitions of complete multipartite graphs.
Keywords: Mathematics; Graph theory