2009/09/07 by Yuanan Diao, Diao, Yuanan, Gabor Hetyei +2
Computer Science · Mathematics · #05C15 #57M25 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #math.AT #math.CO #msc:05C15 #msc:57M25 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0909.1301
22 pages, 6 figures
arxiv created 2009/09/07 · openalex publication_date 2009/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the concept of a relative Tutte polynomial of colored graphs. We show that this relative Tutte polynomial can be computed in a way similar to the classical spanning tree expansion used by Tutte in his original paper on this subject. We then apply the relative Tutte polynomial to virtual knot theory. More specifically, we show that the Kauffman bracket polynomial (hence the Jones polynomial) of a virtual knot can be computed from the relative Tutte polynomial of its face (Tait) graph with some suitable variable substitutions. Our method offers an alternative to the ribbon graph approach, using the face graph obtained from the virtual link diagram directly.