Affiliation:
1. National Institute of Informatics, Tokyo, Japan
2. University of Copenhagen, Copenhagen, Denmark
Abstract
We consider the problem of coloring a 3-colorable graph in polynomial time using as few colors as possible. We first present a new combinatorial algorithm using
Õ
(
n
4/11
) colors. This is the first combinatorial improvement since Blum’s
Õ
(
n
3/8
) bound from FOCS’90. Like Blum’s algorithm, our new algorithm composes immediately with recent semi-definite programming approaches, and improves the best bound for the polynomial time algorithm for the coloring of 3-colorable graphs from
O
(
n
0.2072
) colors by Chlamtac from FOCS’07 to
O
(
n
0.2049
) colors.
Next, we develop a new recursion tailored for combination with semi-definite approaches, bringing us further down to
O
(
n
0.19996
) colors.
Funder
Advanced Grant from the Danish Council for Independent Research under the Sapere Aude research carrier programme
JST ERATO Kawarabayashi Large Graph Project
AT8T Labs--Research
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
15 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Semidefinite Programming and Linear Equations vs. Homomorphism Problems;Proceedings of the 56th Annual ACM Symposium on Theory of Computing;2024-06-10
2. Better Coloring of 3-Colorable Graphs;Proceedings of the 56th Annual ACM Symposium on Theory of Computing;2024-06-10
3. Robust Factorizations and Colorings of Tensor Graphs;SIAM Journal on Discrete Mathematics;2024-02-28
4. Improved NP-Hardness of Approximation for Orthogonality Dimension and Minrank;SIAM Journal on Discrete Mathematics;2023-11-14
5. Graph Colouring Is Hard on Average for Polynomial Calculus and Nullstellensatz;2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS);2023-11-06