PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 69(83), pp. 34--40 (2001)
ON DEGREE SEQUENCES OF GRAPHS WITH GIVEN CYCLOMATIC NUMBER
Manfred SchockerMathematisches Seminar der Universität, Ludewig-Meyn-Str. 4 24098 Kiel, Germany
Abstract: Starting with the Criterion by Gutman and Ruch for graphical partitions, Gutman analyzed degree sequences of connected graphs with cyclomatic number $c$, for $c\le 5$. In this paper, his results are revisited and, based on the Erdös-Gallai Criterion, extended to arbitrary values of $c$. Necessary and sufficient conditions are obtained for any partition to be the degree sequence of a connected graph with cyclomatic number $c$.
Classification (MSC2000): 05C75
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