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2007 Proceedings of the Fourth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

A Characterization of the Degree Sequences of 2-Trees

Abstract

A graph G is a 2-tree if G = K3, or G has a vertex v of degree 2, whose neighbours are adjacent, and G\v is a 2-tree. A characterization of the degree sequences of 2-trees is given. This characterization yields a linear-time algorithm for recognizing and realizing degree sequences of 2-trees.

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Information

Published In

cover image Proceedings
2007 Proceedings of the Fourth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)
Pages: 232 - 241
Editors: Daniel Panario, Carleton University, Ottawa, Ontario, Canada and Robert Sedgewick, Princeton University, Princeton, New Jersey
ISBN (Online): 978-1-61197-297-9

History

Published online: 18 December 2013

Keywords

  1. degree sequence
  2. graphical degree sequence
  3. 2-tree
  4. k-tree
  5. series-parallel graph
  6. treewidth

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Notes

The authors are partly supported by NSERC.
The author is supported by NSERC, Centre de Recherches Mathématiques (CRM), and Institut des Sciences Mathématiques (ISM).
The author is supported by a Marie Curie Fellowship of the European Community under contract 023865, and by the projects MCYT-FEDER BFM2003-00368 and Gen. Cat 2001SGR00224.

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