Convex embeddings and bisections of 3-connected graphs

Hiroshi Nagamochi, T. Jordán, Yoshitaka Nakao, Toshihide Ibaraki

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Given two disjoint subsets T1 and T2 of nodes in an undirected 3-connected graph G = (V, E) with node set V and arc set E, where |T1| and |T2| are even numbers, we show that V can be partitioned into two sets V1 and V2 such that the graphs induced by V1 and V2 are both connected and |V1∩Tj| = |V2∩Tj| = |Tj|/2 holds for each j = 1, 2. Such a partition can be found in O(|V|2log|V|) time. Our proof relies on geometric arguments. We define a new type of 'convex embedding' of k-connected graphs into real space Rk-1 and prove that for k = 3 such an embedding always exists.

Original languageEnglish
Pages (from-to)537-554
Number of pages18
JournalCombinatorica
Volume22
Issue number4
DOIs
Publication statusPublished - 2002

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Bisection
Connected graph
Even number
Vertex of a graph
Disjoint
Arc of a curve
Partition
Subset
Graph in graph theory

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics

Cite this

Convex embeddings and bisections of 3-connected graphs. / Nagamochi, Hiroshi; Jordán, T.; Nakao, Yoshitaka; Ibaraki, Toshihide.

In: Combinatorica, Vol. 22, No. 4, 2002, p. 537-554.

Research output: Contribution to journalArticle

Nagamochi, Hiroshi ; Jordán, T. ; Nakao, Yoshitaka ; Ibaraki, Toshihide. / Convex embeddings and bisections of 3-connected graphs. In: Combinatorica. 2002 ; Vol. 22, No. 4. pp. 537-554.
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