Even cycle decompositions of 4-regular graphs and line graphs

An even cycle decomposition of a graph is a partition of its edge into even cycles. We first give some results on the existence of even cycle decomposition in general 4-regular graphs, showing that ...

[1]  Paul D. Seymour.  Even circuits in planar graphs , 1981, J. Comb. Theory, Ser. B.

[2]  Myriam Preissmann,et al.  Even polyhedral decompositions of cubic graphs , 1980, Discret. Math..

[3]  R. Isaacs.  Infinite Families of Nontrivial Trivalent Graphs Which are not Tait Colorable , 1975 .

[4]  Romeo Rizzi.  On 4-connected graphs without even cycle decompositions , 2001, Discret. Math..

[5]  Cun-Quan Zhang.  On even circuit decompositions of Eulerian graphs , 1994 .

[6]  C. Godsil,et al.  Cycles in graphs , 1985 .

[7]  Martin Kochol,et al.  Five Cycle Double Covers of Some Cubic Graphs , 1995, J. Comb. Theory, Ser. B.

[8]  G. Szekeres,et al.  Polyhedral decompositions of cubic graphs , 1973, Bulletin of the Australian Mathematical Society.

[9]  Nicholas C. Wormald,et al.  Random Matchings Which Induce Hamilton Cycles and Hamiltonian Decompositions of Random Regular Graphs , 2001, J. Comb. Theory, Ser. B.

[10]  J. Petersen.  Die Theorie der regulären graphs , 1891 .

[11]  Melody Chan.  A survey of the cycle double cover conjecture , 2009 .

[12]  Herbert Fleischner,et al.  (Some of) the many uses of Eulerian graphs in graph theory (plus some applications) , 2001, Discret. Math..

[13]  Béla Bollobás,et al.  A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs , 1980, Eur. J. Comb..

[14]  Roland Häggkvist,et al.  Double covers of cubic graphs with oddness 4 , 2005, J. Comb. Theory, Ser. B.

[15]  Carsten Thomassen,et al.  Reflections on graph theory , 1986, J. Graph Theory.

[16]  Andreas Huck.  On cycle-double covers of graphs of small oddness , 2001, Discret. Math..

[17]  Klas Markström,et al.  Complete Minors in Cubic Graphs with few short Cycles and Random Cubic Graphs , 2004, Ars Comb..

[18]  Daniela Kühn,et al.  Minors in random regular graphs , 2008, Random Struct. Algorithms.

[19]  Bill Jackson.  On circuit covers, circuit decompositions and Euler tours of graphs , 1993 .