2015/09/01 by Vincent Despré, Despré, Vincent, Francis Lazarus +1
Computer Science · #05C10 #57M07 #68R99 #Computational Geometry (cs.CG) #Discrete Mathematics (cs.DM) #F.2.2 #FOS: Computer and information sciences #G.2.1 #G.2.2 #acm:05C10 #acm:57M07 #acm:68R99 #cs.CG #cs.DM #msc:05C10 #msc:57M07 #msc:68R99
paper · pdf · doi:10.48550/arxiv.1509.00269
15 pages, 7 figures
arxiv created 2015/09/01 · arxiv updated 2015/09/02
Let G be the graph of a triangulated surface Σ of genus g≥ 2. A cycle of G is splitting if it cuts Σ into two components, neither of which is homeomorphic to a disk. A splitting cycle has type k if the corresponding components have genera k and g-k. It was conjectured that G contains a splitting cycle (Barnette '1982). We confirm this conjecture for an infinite family of triangulations by complete graphs but give counter-examples to a stronger conjecture (Mohar and Thomassen '2001) claiming that G should contain splitting cycles of every possible type.