Alternative links, homogeneous links, and graphs
Jeremy Siegert
TL;DR
This paper reviews the concepts of homogeneous and alternative links, providing new characterizations using enhanced checkerboard graphs and labeled Seifert graphs to deepen understanding of their structures.
Contribution
It introduces two novel characterizations of alternative link diagrams, expanding the theoretical framework within knot theory.
Findings
New characterizations of alternative links
Enhanced checkerboard graph approach
Labeled Seifert graph approach
Abstract
In this paper we review the definitions of homogeneous and alternative links. We also give two new characterizations of an alternative link diagram, one within the context of the enhanced checkerboard graph and another from the labeled Seifert graph.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Graph Theory Research · Advanced Combinatorial Mathematics