4 papers · 1 filter
Almost Series-Parallel graphs: structure and colorability
Elad Aigner-Horev
The series-parallel (SP) graphs are those containing no topological and are considered trivial. We relax the prohibition distinguishing the SP graphs by forbidding only em…
Extremal results regarding -minors in graphs of girth at least 5
Elad Aigner-Horev, Roi Krakovski
We prove that every 6-connected graph of girth has a -minor and thus settle the Jorgensen conjecture for graphs of girth . Relaxing the assumption on the gir…
The Kelmans-Seymour conjecture for apex graphs
Elad Aigner-Horev, Roi Krakovski
We provide a short proof that a 5-connected nonplanar apex graph contains a subdivided or a (= with a single edge removed) as a subgraph. Together with…
Subdivisions in apex graphs
Elad Aigner-Horev
The Kelmans-Seymour conjecture states that the 5-connected nonplanar graphs contain a subdivided . Certain questions of Mader propose a "plan" towards a possible resolution…