Conservative weightings and ear-decompositions of graphs

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

A subset J of edges of a connected undirected graph G=(V, E) is called a join if |C∩J|≤|C|/2 for every circuit C of G. Answering a question of P. Solé and Th. Zaslavsky, we derive a min-max formula for the maximum cardinality μ of a joint of G. Namely, μ=(φ+|V|-1)/2 where φ denotes the minimum number of edges whose contraction leaves a factor-critical graph. To study these parameters we introduce a new decomposition of G, interesting for its own sake, whose building blocks are factor-critical graphs and matching-covered bipartite graphs. We prove that the length of such a decomposition is always φ and show how an optimal join can be constructed as the union of perfect matchings in the building blocks. The proof relies on the Gallai-Edmonds structure theorem and gives rise to a polynomial time algorithm to construct the optima in question.

Original languageEnglish
Pages (from-to)65-81
Number of pages17
JournalCombinatorica
Volume13
Issue number1
DOIs
Publication statusPublished - Mar 1993

Fingerprint

Factor Graph
Critical Graph
Building Blocks
Join
Weighting
Decomposition
Decompose
Structure Theorem
Perfect Matching
Graph in graph theory
Sols
Min-max
Undirected Graph
Bipartite Graph
Polynomial-time Algorithm
Connected graph
Contraction
Cardinality
Union
Polynomials

Keywords

  • AMS subject classification code (1991): 05C70, 05C75, 94B60

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

Conservative weightings and ear-decompositions of graphs. / Frank, A.

In: Combinatorica, Vol. 13, No. 1, 03.1993, p. 65-81.

Research output: Contribution to journalArticle

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