Packing A-paths of length zero modulo four

We show that A-paths of length 0 modulo 4 have the Erd\H{o}s-P\'osa property. We also prove that A-paths of length 2 modulo 4 have the property but that A-paths of length 1 or of length 3 modulo 4 do not have it.

[1]  Bruce A. Reed,et al.  Packing directed circuits , 1996, Comb..

[2]  Dimitrios M. Thilikos,et al.  Recent techniques and results on the Erdős-Pósa property , 2016, Discret. Appl. Math..

[3]  J. A. Bondy,et al.  Graph Theory , 2008, Graduate Texts in Mathematics.

[4]  Matthias Kriesell,et al.  Disjoint A-paths in digraphs , 2005, Journal of combinatorial theory. Series B (Print).

[5]  Paul Wollan,et al.  Packing non-zero A-paths in an undirected model of group labeled graphs , 2010, J. Comb. Theory, Ser. B.

[6]  Carsten Thomassen,et al.  On the presence of disjoint subgraphs of a specified type , 1988, J. Graph Theory.

[7]  Robin Thomas,et al.  Quickly Excluding a Planar Graph , 1994, J. Comb. Theory, Ser. B.

[8]  Chun-Hung Liu Packing Topological Minors Half-Integrally , 2017, ArXiv.

[9]  Ken-ichi Kawarabayashi,et al.  The Directed Grid Theorem , 2015, STOC.

[10]  Paul D. Seymour,et al.  Graph Minors: XV. Giant Steps , 1996, J. Comb. Theory, Ser. B.

[11]  Paul D. Seymour,et al.  Graph minors. X. Obstructions to tree-decomposition , 1991, J. Comb. Theory, Ser. B.

[12]  Matthias Kriesell,et al.  Asymptotically optimal K k -packings of dense graphs via fractional K k -decompositions , 2005 .

[13]  Paul Wollan,et al.  A Unified Erdős–Pósa Theorem for Constrained Cycles , 2019, Comb..

[14]  T. Gallai Maximum-Minimum Sätze und verallgemeinerte Faktoren von Graphen , 1964 .

[15]  Paul Wollan,et al.  Packing cycles with modularity constraints , 2011, Comb..

[16]  Henning Bruhn,et al.  Frames, A-Paths, and the Erdös-Pósa Property , 2018, SIAM J. Discret. Math..

[17]  P. Erdös,et al.  On Independent Circuits Contained in a Graph , 1965, Canadian Journal of Mathematics.

[18]  Paul D. Seymour,et al.  Graph minors. V. Excluding a planar graph , 1986, J. Comb. Theory B.