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Tutte's 5-flow conjecture for graphs of nonorientable genus 5

✍ Scribed by Steffen, Eckhard

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 577 KB
Volume: 22
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199608)22:4<309::aid-jgt5>3.0.co;2-p

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✦ Synopsis

We develop four constructions for nowhere-zero 5-flows of 3-regular graphs that satisfy special structural conditions. Using these constructions we show a minimal counterexample to Tutte's 5-Flow Conjecture is of order 244 and therefore every bridgeless graph of nonorientable genus 5 5 has a nowhere-zero 5-flow.

One of the structural properties is formulated in terms of the structure of the multigraph G ( F ) obtained from a given 3-regular graph G by contracting the cycles of a 2-factor F in G.

📜 SIMILAR VOLUMES

Tutte's 5-flow conjecture for the projec

Tutte's 5-flow conjecture for the projective plane

✍ Richard Steinberg 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 300 KB

Heawood proved that every planar graph with no 1-cycles is vertex 5colorable, which is equivalent to the statement that every planar graph with no 1-bonds has a nowhere-zero 5-flow. Tutte has conjectured that every graph with no 1-bonds has a nowhere-zero 5-flow. We show that Tutte's 5-Flow Conjectu