Title:
On Locally-Balanced 2-Partitions of Some Graphs
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Uncontrolled Keywords:
Locally-balanced 2-partition ; equitable coloring ; Eulerian graph ; rook’s graph ; power of cycles
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.
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Additional Information:
aramgharibyan@gmail.com ; pet petros@ipia.sci.am
Affiliation:
Yerevan State University ; Department of Informatics and Applied Mathematics ; Institute for Informatics and Automation Problems
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Conference title:
11th International Conference on Computer Science and Information Technologies CSIT 2017