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On 3-Coloring of ( )-Free Graphs
Vít Jelínek1, Tereza Klimošová1, Tomáš Masařík1,2,3
1Faculty of Mathematics and Physics, Charles University, Malostranské Náměstí 25, 11800 Prague, Czech Republic.
Algorithmica
|June 2, 2022
Summary
This study solves the 3-coloring problem for a specific type of graph called P8-free graphs. This finding advances the understanding of graph coloring complexity for hereditary graph classes.
Area of Science:
- Graph Theory
- Computational Complexity
Background:
- The 3-coloring problem for hereditary graph classes is a significant area of research.
- Complexity is known for H-free graphs up to seven vertices, with two unsolved cases on eight vertices.
Purpose of the Study:
- To investigate the complexity of the 3-coloring problem for P8-free graphs.
- To determine if 3-coloring is efficiently solvable for this previously unexplored class.
Main Methods:
- The study focuses on P8-free graphs, a class defined by forbidden induced subgraphs.
- Algorithmic techniques are employed to develop a polynomial-time solution.
Main Results:
- The 3-coloring problem is proven to be polynomial-time solvable for P8-free graphs.
- This resolves one of the remaining open cases in the complexity of 3-coloring for H-free graphs.
Conclusions:
- The 3-coloring problem is efficiently solvable on P8-free graphs.
- This contributes to a more complete understanding of graph coloring complexity in hereditary graph classes.
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