4 papers
Characterization and chromatic number of triangle-free graphs with diameter 2
Akihiro Higashitani, Diogo Kendy Matsumoto, Naoki Matsumoto
In this paper, we consider triangle-free graphs with diameter 2. If a triangle-free graph with diameter 2 is not isomorphic to a star, then the radius of is also 2, where s…
Travel groupoids on complete multipartite graphs
Diogo Kendy Matsumoto
A travel groupoid is an algebraic system satisfying two suitable conditions, which has a relation to graphs. In this article, we characterize travel groupoids on finite complete mu…
Quiver-theoretical approach to dynamical Yang-Baxter maps
Diogo Kendy Matsumoto, Kenichi Shimizu
A dynamical Yang-Baxter map, introduced by Shibukawa, is a solution of the set-theoretical analogue of the dynamical Yang-Baxter equation. In this paper, we initiate a quiver-theor…
Combinatorial aspects of dynamical Yang-Baxter maps and dynamical braces
Diogo Kendy Matsumoto
In this article we propose an algebraic system, which is an abelian group with a family of non-associative and non-(left)distributive multiplications …