The Kelmans-Seymour conjecture I: Special separations

Journal of Combinatorial Theory, Series B - Tập 144 - Trang 197-224 - 2020
Dawei He1, Yan Wang2, Xingxing Yu2
1Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China
2School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States of America

Tài liệu tham khảo

Chakravarti, 1979, Covering three edges with a bond in a nonseparable graph, 247 Kawarabayashi, 2002, Contractible edges and triangles in k-connected graphs, J. Comb. Theory, Ser. B, 85, 207, 10.1006/jctb.2001.2096 Kawarabayashi, 2015, Subdivisions of K5 in graphs containing K2,3, J. Comb. Theory, Ser. B, 113, 18, 10.1016/j.jctb.2014.12.008 Kelmans, 1979, Every minimal counterexample to the Dirac conjecture is 5-connected Ma, 2010, Independent paths and K5-subdivisions, J. Comb. Theory, Ser. B, 100, 600, 10.1016/j.jctb.2010.05.002 Ma, 2013, K5-subdivisions in graphs containing K4− (with J. Ma), J. Comb. Theory, Ser. B, 103, 713, 10.1016/j.jctb.2013.09.006 Ma, 2016, Graphs containing topological H, J. Graph Theory, 82, 121, 10.1002/jgt.21891 Perfect, 1968, Applications of Menger's graph theorem, J. Math. Anal. Appl., 22, 96, 10.1016/0022-247X(68)90163-7 Seymour, 1980, Disjoint paths in graphs, Discrete Math., 29, 293, 10.1016/0012-365X(80)90158-2 P.D. Seymour, Private communication with X. Yu. Shiloach, 1980, A polynomial solution to the undirected two paths problem, J. Assoc. Comput. Mach., 27, 445, 10.1145/322203.322207 Thomassen, 1980, 2-Linked graphs, Eur. J. Comb., 1, 371, 10.1016/S0195-6698(80)80039-4 Watkins, 1967, Cycles and connectivity in graphs, Can. J. Math., 19, 1319, 10.4153/CJM-1967-121-2