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arXiv · 1511.05847

Trees with small b-chromatic index

Ana Silva
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Abstract

In a recent article [5], the authors claim that the distance between the b-chromatic index of a tree and a known upper bound is at most 1. At the same time, in [7] the authors claim to be able to construct a tree where this difference is bigger than 1. However, the given example was disconnected, i.e., actually consisted of a forest. Here, we slightly modify their construction in order to produce trees, thus getting that indeed the difference between the b-chromatic index of trees and the known upper bound can be arbitrarily large. We also point out the mistake made in [5].

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Ana Silva. 2015-11-18. Trees with small b-chromatic index. https://arxiv.org/abs/1511.05847

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