2012/03/09 by Jonas Hägglund, Hägglund, Jonas
Computer Science · Mathematics · #05C70 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO #msc:05C70
paper · pdf · doi:10.48550/arxiv.1203.2015
10 pages, 7 figures
arxiv created 2012/03/09 · arxiv updated 2012/03/12
In this note we construct two infinite snark families which have high oddness and low circumference compared to the number of vertices. Using this construction, we also give a counterexample to a suggested strengthening of Fulkerson's conjecture by showing that the Petersen graph is not the only cyclically 4-edge connected cubic graph which require at least five perfect matchings to cover its edges. Furthermore the counterexample presented has the interesting property that no 2-factor can be part of a cycle double cover.