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arXiv · 1512.08448

On degree sequences of undirected, directed, and bidirected graphs

Laura Gellert·Raman Sanyal
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Abstract

Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we extend the following four topics from (un)directed graphs to bidirected graphs: - Erdős-Gallai-type results: characterization of net-degree sequences, - Havel-Hakimi-type results: complete sets of degree-preserving operations, - Extremal degree sequences: characterization of uniquely realizable sequences, and - Enumerative aspects: counting formulas for net-degree sequences. To underline the similarities and differences to their (un)directed counterparts, we briefly survey the undirected setting and we give a thorough account for digraphs with an emphasis on the discrete geometry of degree sequences. In particular, we determine the tight and uniquely realizable degree sequences for directed graphs.

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Laura Gellert, Raman Sanyal. 2017-04-10. On degree sequences of undirected, directed, and bidirected graphs. https://arxiv.org/abs/1512.08448

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