3‐Flows and Combs. Issue 4 (14th January 2014)

• Record Type: Journal Article
• Authors: da Silva, Cândida Nunes; Lucchesi, Cláudio L.
• Is Part Of: Journal of graph theory. Volume 77:Issue 4(2014)
• Page Start: 260
• Page End: 277
• Publication Date: 2014-01-14
• Subjects: Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.21785
• Languages: English
• ISSNs: 0364-9024

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>Tutte's 3‐Flow Conjecture states that every 2‐edge‐connected graph with no 3‐cuts admits a 3‐flow. The 3‐Flow Conjecture is equivalent to the following: let <italic>G</italic> be a 2‐edge‐connected graph, let <italic>S</italic> be a set of at most three vertices of <italic>G</italic>; if every 3‐cut of <italic>G</italic> separates <italic>S</italic> then <italic>G</italic> has a 3‐flow. We show that minimum counterexamples to the latter statement are 3‐connected, cyclically 4‐connected, and cyclically 7‐edge‐connected.</p> </abstract>