Mingxian Zhong

4-Coloring P6-Free Graphs with No Induced 5-Cycles†

We show that the 4-coloring problem can be solved in polynomial time for graphs with no induced 5-cycle C5 and no induced 6-vertex path P6

Three-Coloring and List Three-Coloring of Graphs Without Induced Paths on Seven Vertices

In this paper we present a polynomial time algorithm that determines if an input graph containing no induced seven-vertex path is 3-colorable. This affirmatively answers a question posed by Randerath, Schiermeyer and Tewes in 2002. Our algorithm also solves the list-coloring version of the 3-coloring problem, where every vertex is assigned a list of colors that is a subset of {1,2,3}, and gives an explicit coloring if one exists.

Triangle-free graphs with no six-vertex induced path

Abstract The graphs with no five-vertex induced path are still not understood. But in the triangle-free case, we can do this and one better; we give an explicit construction for all triangle-free graphs with no six-vertex induced path. Here are three examples: the 16-vertex Clebsch graph, the graph obtained from an 8-cycle by making opposite vertices adjacent, and the graph obtained from a complete bipartite graph by subdividing a perfect matching. We show that every connected triangle-free graph with no six-vertex induced path is an induced subgraph of one of these three (modulo some twinning and duplication).

Approximately Coloring Graphs Without Long Induced Paths

It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on

Three-coloring graphs with no induced seven-vertex path II : using a triangle.

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Obstructions for three-coloring graphs with one forbidden induced subgraph

vertices, for fixed

Three-coloring graphs with no induced seven-vertex path I : the triangle-free case.

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Obstructions for three-coloring graphs without induced paths on six vertices.

. We propose an algorithm that, given a 3-colorable graph without an induced path on

Four-coloring Ps 6 -free graphs. I. Extending an excellent precoloring.

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Four-coloring P 6 -free graphs. II. Finding an excellent precoloring.

vertices, computes a coloring with