2 citations · 2 across the 4 of their papers we have counts for
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Cayley graphs of abelian groups, circular colorings and discrete fundamental groups
Kengo Enami, Takahiro Matsushita
For each integer , we prove that an abelian group satisfies if and only if it admits no non-bipartite Cayley graph wh…
Non-uniqueness of optimal -embeddings on surfaces up to weak equivalence
Kengo Enami
We study the uniqueness of optimal -embeddings on closed surfaces up to weak equivalence. Answering a question of Suzuki in the negative, we show that for every closed surface o…
Higher-dimensional generalization of Youngs' theorem and circular colorings
Kengo Enami, Takahiro Matsushita
In 1996, Youngs proved that any quadrangulation of the real projective plane is not 3-chromatic. This result has been extended in various directions over the years, including to ot…
Difference of facial achromatic numbers between two triangular embeddings of a graph
Kengo Enami, Yumiko Ohno
A facial -complete -coloring of a triangulation on a surface is a vertex -coloring such that every triple of -colors appears on the boundary of some face of . Th…
Embeddings of 3-connected 3-regular planar graphs on surfaces of non-negative Euler characteristic
Kengo Enami
Whitney's theorem states that every 3-connected planar graph is uniquely embeddable on the sphere. On the other hand, it has many inequivalent embeddings on another surface. We sha…