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math.CO2016
Decomposing planar cubic graphs
Arthur Hoffmann-Ostenhof, Tomáš Kaiser, Kenta Ozeki
The 3-Decomposition Conjecture states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular subgraph and a matching. We show that this conjecture hol…
math.CO2016
A Note on -colorings of Quadrangulations
Arthur Hoffmann-Ostenhof, Atsuhiro Nakamoto
Let be a quadrangulation on an orientable surface and let be a proper vertex--coloring of . A face of is said to be a rainbow-face if all four distinct colors…