Graphs with small balanced decomposition numbers

Hsiang-Chun Hsu () and Gerard Jennhwa Chang ()
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Hsiang-Chun Hsu: National Taiwan University
Gerard Jennhwa Chang: National Taiwan University

Journal of Combinatorial Optimization, 2014, vol. 28, issue 2, No 12, 505-510

Abstract: Abstract A balanced coloring of a graph $$G$$ is an ordered pair $$(R,B)$$ of disjoint subsets $$R,B \subseteq V(G)$$ with $$|R|=|B|$$ . The balanced decomposition number $$f(G)$$ of a connected graph $$G$$ is the minimum integer $$f$$ such that for any balanced coloring $$(R,B)$$ of $$G$$ there is a partition $$\mathcal{P}$$ of $$V(G)$$ such that $$S$$ induces a connected subgraph with $$|S| \le f$$ and $$|S \cap R| = |S \cap B|$$ for $$S \in \mathcal{P}$$ . This paper gives a short proof for the result by Fujita and Liu (2010) that a graph $$G$$ of $$n$$ vertices has $$f(G)=3$$ if and only if $$G$$ is $$\lfloor \frac{n}{2} \rfloor $$ -connected but is not a complete graph.

Keywords: Balanced coloring; Balanced decomposition; Balanced decomposition number; Connectivity (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9576-6

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