# Coloring Problems on Bipartite Graphs of Small Diameter

@article{Campos2021ColoringPO, title={Coloring Problems on Bipartite Graphs of Small Diameter}, author={Victor A. Campos and Guilherme Gomes and Allen Ibiapina and Raul Lopes and Ignasi Sau and Ana Silva}, journal={Electron. J. Comb.}, year={2021}, volume={28}, pages={2} }

We investigate a number of coloring problems restricted to bipartite graphs with bounded diameter. First, we investigate the $k$-List Coloring, $k$-Coloring, and $k$-Precoloring Extension problems on bipartite graphs with diameter at most $d$, proving $\textsf{NP}$-completeness in most cases, and leaving open only the List $3$-Coloring and $3$-Precoloring Extension problems when $d=3$.
Some of these results are obtained $\textsc{through}$ a proof that the Surjective $C_6$-Homomorphism problem…

## 2 Citations

### Faster 3-coloring of small-diameter graphs

- Mathematics, Computer ScienceESA
- 2021

This paper presents an algorithm that solves 3-Coloring in n-vertex diameter-2 graphs in time 2^{𝒪(n 1/3} log² n)}.

### Fully Dynamic (Δ +1)-Coloring in O(1) Update Time

- Mathematics, Computer ScienceACM Trans. Algorithms
- 2022

An improved randomized algorithm for (Δ +1)-coloring that achieves O(1) amortized update time and it is shown that this bound holds not only in expectation but also with high probability.

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