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A note on shortest cycle covers of cubic graphs
Author(s) -
Hou Xinmin,
Zhang CunQuan
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.20636
Subject(s) - combinatorics , mathematics , cubic graph , disjoint sets , odd graph , graph , discrete mathematics , girth (graph theory) , upper and lower bounds , chordal graph , 1 planar graph , line graph , voltage graph , mathematical analysis
Let SCC 3 ( G ) be the length of a shortest 3‐cycle cover of a bridgeless cubic graph G . It is proved in this note that if G contains no circuit of length 5 (an improvement of Jackson's ( JCTB 1994 ) result: if G has girth at least 7) and if all 5‐circuits of G are disjoint (a new upper bound of SCC 3 ( G ) for the special class of graphs).