Kempe Equivalence of Edge‐Colorings in Subcubic and Subquartic Graphs | Zendy

McDonald Jessica | Zendy; Mohar Bojan | Zendy; Scheide Diego | Zendy

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Kempe Equivalence of Edge‐Colorings in Subcubic and Subquartic Graphs

Author(s) -

McDonald Jessica,

Mohar Bojan,

Scheide Diego

Publication year - 2012

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.20613

Subject(s) - mathematics , combinatorics , conjecture , equivalence (formal languages) , edge coloring , graph , enhanced data rates for gsm evolution , cubic graph , discrete mathematics , line graph , voltage graph , graph power , computer science , telecommunications

It is proved that all 4‐edge‐colorings of a (sub)cubic graph are Kempe equivalent. This resolves a conjecture of the second author. In fact, it is found that the maximum degree Δ = 3 is a threshold for Kempe equivalence of (Δ+1)‐edge‐colorings, as such an equivalence does not hold in general when Δ = 4. One extra color allows a similar result in this latter case; however, namely, when Δ≤4 it is shown that all (Δ+2)‐edge‐colorings are Kempe equivalent. © 2011 Wiley Periodicals, Inc. J Graph Theory

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