Geodesic
On Degree Sequences of Graphs with Given Cyclomatic Number
Publications de l'Institut Mathématique, _N_S_69 (2001) no. 83, p. 34

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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 : 05C75 
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     author = {Manfred Schocker},
     title = {On {Degree} {Sequences} of {Graphs} with {Given} {Cyclomatic} {Number}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {34 },
     publisher = {mathdoc},
     volume = {_N_S_69},
     number = {83},
     year = {2001},
     zbl = {0997.05028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a5/}
}
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Manfred Schocker. On Degree Sequences of Graphs with Given Cyclomatic Number. Publications de l'Institut Mathématique, _N_S_69 (2001) no. 83, p. 34 . http://geodesic.mathdoc.fr/item/PIM_2001_N_S_69_83_a5/