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arXiv · 2309.12670

Weak degeneracy of regular graphs

Yuxuan Yang
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Abstract

Motivated by the study of greedy algorithms for graph coloring, Bernshteyn and Lee introduced a generalization of graph degeneracy, which is called weak degeneracy. In this paper, we show the lower bound of the weak degeneracy for $d$-regular graphs is exactly $\lfloor d/2\rfloor +1$, which is tight. This result refutes the conjecture of Bernshteyn and Lee on this lower bound.

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Yuxuan Yang. 2023-09-29. Weak degeneracy of regular graphs. https://arxiv.org/abs/2309.12670

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