Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Short and local transformations between ($Δ+1$)-colorings (2203.08885v2)

Published 16 Mar 2022 in cs.DM, cs.DC, cs.DS, and math.CO

Abstract: Recoloring a graph is about finding a sequence of proper colorings of this graph from an initial coloring $\sigma$ to a target coloring $\eta$. Adding the constraint that each pair of consecutive colorings must differ on exactly one vertex, one asks: Is there a sequence of colorings from $\sigma$ to $\eta$? If yes, how short can it be? In this paper, we focus on $(\Delta+1)$-colorings of graphs of maximum degree $\Delta$. Feghali, Johnson and Paulusma proved that, if both colorings are non-frozen (i.e. we can change the color of a least one vertex), then a quadratic recoloring sequence always exists. We improve their result by proving that there actually exists a linear transformation (assuming that $\Delta$ is a constant). In addition, we prove that the core of our algorithm can be performed locally. Informally, this means that after some preprocessing, the color changes that a given node has to perform only depend on the colors of the vertices in a constant size neighborhood. We make this precise by designing of an efficient recoloring algorithm in the LOCAL model of distributed computing.

Citations (3)

Summary

We haven't generated a summary for this paper yet.