LOCALLY-BALANCED k-PARTITIONS OF GRAPHS - Gharibyan, Aram H.; Petrosyan, Petros A. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2021)
In this paper we generalize locally-balanced 2-partitions of graphs and introduce a new notion, the locally-balanced k-partitions of graphs, defined as follows: a k-partition of a graph G is a surjection $f:V(G)→ \{0,1,…,k-1\}$. A k-partition (k$≥ $2) f of a graph G is a locally-balanced with an open neighborhood, if for every $v\in V(G)$ and any $0≤ i
Keywords: $2$-partition; $k$-partition; locally-balanced $k$-partition; complete graph; biregular bipartite graph