The Minimal Coloring Number Of Any Non-splittable $\mathbb{Z}$-colorable Link Is Four

Zhang, Meiqiao; X, Jin; Deng, Qingying

doi:10.48550/arxiv.1706.08837

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2019

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Cited by 2 publications

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“…The minimal coloring number of any non-splittable Z-colorable link is equal to 4. This result is also proved by Meiqiao Zhang, Xian'an Jin and Qingying Deng almost independently in [4]. Previously Zhang gave us her manuscript for her Master thesis.…”

Section: Introductionmentioning

confidence: 59%

See 1 more Smart Citation

Minimal coloring number for ℤ-colorable links II

Matsudo

2019

J. Knot Theory Ramifications

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The minimal coloring number of a Z-colorable link is the minimal number of colors for non-trivial Z-colorings on diagrams of the link. In this paper, we show that the minimal coloring number of any non-splittable Z-colorable links is four. As an example, we consider the link obtained by replacing each component of the given link with several parallel strands, which we call a parallel of a link. We show that an even parallel of a link is Z-colorable except for the case of 2 parallels with non-zero linking number. We then give a simple way to obtain a diagram which attains the minimal coloring number for such even parallels of links.

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Section: Introductionmentioning

confidence: 59%

“…We can find a path on D from a d m -diff crossing to a d-diff crossing passing only 0-diff crossings with 0 < d < d m . Such a path is one of the 4 types [1], [2], [3] and [4] illustrated in Figure 1.…”

Section: Main Theoremmentioning

confidence: 99%