To accelerate research on Beyond 5G (B5G) technologies in Japan, we propose an
algorithm that designs mesh-type metropolitan area network (MAN) models based on a …

Motivated by anti-Ramsey numbers introduced by Erdős, Simonovits and Sós in 1975, we
study the anti-Ramsey problem when host graphs are plane triangulations. Given a positive …

In this survey the following types of colorings of plane graphs are discussed, both in their
vertex and edge versions: facially proper coloring, rainbow coloring, antirainbow coloring …

In the article, the existence of rainbow cycles in edge colored plane triangulations is studied.
It is shown that the minimum number of colors that force the existence of a rainbow C3 in any …

Given a positive integer n and a planar graph H, let T n (H) be the family of all plane
triangulations T on n vertices such that T contains a subgraph isomorphic to H. The planar …

We call a subgraph of an edge-colored graph rainbow, if all of its edges have different
colors. A rainbow copy of a graph H in an edge-colored graph G is a subgraph of G …

It is shown that whenever the edges of a connected simple graph on n vertices are colored
with n-1 n-1 colors appearing so that no cycle in G is rainbow, there must be a …

A face of an edge colored plane graph is called e-loose if the number of colors used on its
edges is at least three. The e-looseness of a plane graph G is the minimum positive integer k …

We consider, for a plane graph G and a positive integer p, an edge coloring such that the set
of colors used on each face of G contains at most p colors. The maximum number of colors …

A facial edge k-ranking of a plane graph G is a labeling of its edges with integers 1,…, k
such that every facial trail connecting two edges with the same label contains an edge with a …