Graph realizations constrained by skeleton graphs

Péter L. Erdős, Stephen G. Hartke, Leo van Iersel, István Miklós

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1 Citation (Scopus)
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In 2008 Amanatidis, Green and Mihail introduced the Joint Degree Matrix (JDM) model to capture the fundamental difference in assortativity of networks in nature studied by the physical and life sciences and social networks studied in the social sciences. In 2014 Czabarka proposed a direct generalization of the JDM model, the Partition Adjacency Matrix (PAM) model. In the PAM model the vertices have specified degrees, and the vertex set itself is partitioned into classes. For each pair of vertex classes the number of edges between the classes in a graph realization is prescribed. In this paper we apply the new skeleton graph model to describe the same information as the PAM model. Our model is more convenient for handling problems with low number of partition classes or with special topological restrictions among the classes. We investigate two particular cases in detail: (i) when there are only two vertex classes and (ii) when the skeleton graph contains at most one cycle.

Original languageEnglish
Article number#P2.47
Pages (from-to)1-18
Number of pages18
JournalThe Electronic Journal of Combinatorics
Issue number2
Publication statusPublished - 2017


  • Degree sequences
  • Edmonds’s blossom algorithm
  • Forbidden edges
  • Joint Degree Matrix
  • Partition Adjacency Matrix
  • Skeleton graph
  • Tutte gadget

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    Erdős, P. L., Hartke, S. G., van Iersel, L., & Miklós, I. (2017). Graph realizations constrained by skeleton graphs. The Electronic Journal of Combinatorics, 24(2), 1-18. [#P2.47].