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P 4 ‐decompositions of regular graphs
Author(s) -
Heinrich Katherine,
Liu Jiping,
Yu Minli
Publication year - 1999
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/(sici)1097-0118(199906)31:2<135::aid-jgt6>3.0.co;2-i
Subject(s) - mathematics , combinatorics , eulerian path , graph , strongly regular graph , discrete mathematics , symmetric graph , 1 planar graph , line graph , pathwidth , voltage graph , pure mathematics , lagrangian
In this article, we show that every simple r ‐regular graph G admits a balanced P 4 ‐decomposition if r ≡ 0(mod 3) and G has no cut‐edge when r is odd. We also show that a connected 4‐regular graph G admits a P 4 ‐decomposition if and only if | E ( G )| ≡ 0(mod 3) by characterizing graphs of maximum degree 4 that admit a triangle‐free Eulerian tour. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 135–143, 1999