HISTs of triangulations on surfaces
Atsuhiro Nakamoto, Shoichi Tsuchiya · AKCE International Journal of Graphs and Combinatorics · 2013
A spanning tree with no vertices of degree two of a graph is called a homeomorphically irreducible spanning tree (or a HIST ) of the graph. In [4], Ellingham has proposed a conjecture that every triangulation on a closed surface with suciently large representativity has a HIST. In this paper, we solve Ellingham’s conjecture. Moreover we prove that every