Geodesic
A Sufficient Condition for Graphic Sequences with Given Largest and Smallest Entries, Length, and Sum
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1.

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We give a sufficient condition for a degree sequence to be graphic based on its largest and smallest elements, length, and sum. This bound generalizes a result of Zverovich and Zverovich. 
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     title = {A {Sufficient} {Condition} for {Graphic} {Sequences} with {Given} {Largest} and {Smallest} {Entries,} {Length,} and {Sum}},
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Cloteaux, Brian. A Sufficient Condition for Graphic Sequences with Given Largest and Smallest Entries, Length, and Sum. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1. doi : 10.23638/DMTCS-20-1-25. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-25/

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