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Congruence classes of monodromies of even triangulations
Kenta Noguchi
A triangulation is a graph on a surface where every face is triangular. It is well-known that a planar triangulation is -chromatic if and only if is even, that is, all t…
Spanning bipartite quadrangulations of triangulations of the projective plane
Kenta Noguchi
We completely characterize triangulations of the projective plane that have a spanning bipartite quadrangulation subgraph. This is an affirmative answer to a question by Kündgen an…
Proper 3-orientations of bipartite planar graphs with minimum degree at least 3
Kenta Noguchi
We show that every bipartite planar graph with minimum degree at least 3 has proper orientation number at most 3.
On Homeomorphically Irreducible Spanning Trees in Cubic Graphs
Arthur Hoffmann-Ostenhof, Kenta Noguchi, Kenta Ozeki
A spanning tree without a vertex of degree two is called a Hist which is an abbreviation for homeomorphically irreducible spanning tree. We provide a necessary condition for the ex…