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Ars Combinatoria

  • Research article

Characterization of \(M_3(2)\)-graphs

S. Akbari1, D. Kiani2,3, F. Mohammadi2, S. Moradi2
1Department of Mathematical Sciences Sharif University of Technology P. O. Box 11365-9415, Tehran, Iran.
2Department of Pure Mathematics, Faculty of Mathematics and Computer Sci- ence, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran.
3Institute for Studies in Theoretical Physics and Mathematics (IPM).
  • Published: 31/07/2013

Abstract

A graph \(G\) is called an \(M_r(k)\)-graph if \(G\) has no \(k\)-list assignment to its vertices with exactly \(r\) vertex colorings. We characterize all \(M_3(2)\)-graphs. More precisely, it is shown that a connected graph \(G\) is an \(M_3(2)\)-graph if and only if each block of \(G\) is a complete graph with at least three vertices.

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Citation
S. Akbari, D. Kiani, F. Mohammadi, S. Moradi. Characterization of \(M_3(2)\)-graphs[J], Ars Combinatoria, Volume 111. 505-513. .