4 papers · 1 filter
The Balanced Four-Color Theorem
Ken-ichi Kawarabayashi, Hirotaka Yoneda, Masataka Yoneda
We show that every planar graph with vertices admits a 4-coloring in which each color is used on fewer than vertices. This bound is the best possible. Moreover, su…
EPTAS for Hard Graph Cut Problems for Dense Graphs
Kaisei Deguchi, Ken-ichi Kawarabayashi, Hiroaki Mori
Everywhere--dense graphs are defined as graphs on vertices in which every vertex has degree at least for some constant . Approximation schemes are vital for handl…
Online Graph Coloring for -Colorable Graphs
Ken-ichi Kawarabayashi, Hirotaka Yoneda, Masataka Yoneda
We study the problem of online graph coloring for -colorable graphs. The best previously known deterministic algorithm uses colors for genera…
Better coloring of 3-colorable graphs
Ken-ichi Kawarabayashi, Mikkel Thorup, Hirotaka Yoneda
We consider the problem of coloring a 3-colorable graph in polynomial time using as few colors as possible. This is one of the most challenging problems in graph algorithms. In thi…