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arXiv · 1304.0083

Characterizations of 2-Colorable (Bipartite) and 3-Colorable Graphs

E. Sampathkumar·M. A. Sriraj
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Abstract

A \emph{directional labeling} of an edge $\emph{uv}$ in a graph $G=(V,E)$ by an ordered pair $ab$ is a labeling of the edge $uv$ such that the label on $uv$ in the direction from $u$ to $v$ is $\ell(uv)=ab$, and $\ell(vu)=ba$. New characterizations of 2-colorable (bipartite) and 3-colorable graphs are obtained in terms of directional labeling of edges of a graph by ordered pairs $ab$ and $ba$. In addition we obtain characterizations of 2-colorable and 3-colorable graphs in terms of matrices called directional adjacency matrices.

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E. Sampathkumar, M. A. Sriraj. 2013-03-30. Characterizations of 2-Colorable (Bipartite) and 3-Colorable Graphs. https://arxiv.org/abs/1304.0083

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