@misc{Gharibyan_Aram_On,
author={Gharibyan Aram},
howpublished={online},
language={English},
abstract={A 2-partition of a graph G is a function f : V (G) → \{0, 1\}. 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) = 1\}| − |\{u ∈ NG(v) : f(u) = 0\}|| ≤ 1, where NG(v) = \{u ∈ V (G): uv ∈ E(G)\}. A 2- partition f 0 of a graph G is locally-balanced with a closed neighborhood if for every v ∈ V (G), ||\{u ∈ NG[v] : f 0 (u) = 1\}| − |\{u ∈ NG[v] : f 0 (u) = 0\}|| ≤ 1, where NG[v] = NG(v) ∪ \{v\}. In this paper we obtain some conditions for the existence of locally-balanced 2- partitions of certain graphs. In particular, we prove some necessary condition for the existence of locallybalanced 2-partitions of Eulerian graphs. Moreover, we also obtain some results on the existence of locallybalanced 2-partitions of rook’s graphs and powers of cycles.},
title={On Locally-Balanced 2-Partitions of Some Graphs},
type={Conference},
}