PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 33(47), pp. 157162 (1983) 

EDGECOLORING OF A FAMILY OF REGULAR GRAPHSBojan Mohar, Tomazh PisanskiDepartment of Mathematics, University of Ljubljana, 61000 Ljubljana, YugoslaviaAbstract: Let $G(m)$ denote the composition graph $G[mK_1]$. An obvious necessary condition for $G(m)$ to be 1factorable is that $G$ is regular and $mp$ is even, where $p$ is the number of vertices of $G$. It is conjectured that this is also a sufficient condition. For regular $G$ it is proved that $G(m)$ is 1factorable if at least one of the following conditions is satisfied: (a) $G$ is 1factorable, (b) $G$ is of even degree and $m$ is even, (c) $m$ is divisible by 4, (d) $G$ has a 1factor and $m$ is even, (e) $G$ is cubic and $m$ is even. The results are used to solve some other problems. Keywords: regular graph, edgecoloring, factorization Classification (MSC2000): 05C15 Full text of the article:
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