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Almost all 5‐regular graphs have a 3‐flow
Author(s) -
Prałat Paweł,
Wormald Nick
Publication year - 2020
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22478
Subject(s) - mathematics , combinatorics , conjecture , discrete mathematics , 1 planar graph , graph , chordal graph
Tutte conjectured in 1972 that every 4‐edge–connected graph has a nowhere‐zero 3‐flow. This has long been known to be equivalent to the conjecture that every 5‐regular 4‐edge–connected graph has an edge orientation in which every in‐degree is either 1 or 4. We show that the assertion of the conjecture holds asymptotically almost surely for random 5‐regular graphs. It follows that the conjecture holds for almost all 4‐edge–connected 5‐regular graphs.