2012/02/20 by Yuanan Diao, Y. DIAO, Gábor Hetyei +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Chromatic polynomial #Graph #Graph theory and applications #Polynomial #Product (mathematics) #Tensor product #Tutte polynomial #math.CO #msc:05C15 #msc:05C35 #msc:57M25
paper · pdf · doi:10.1017/s0963548313000370
published as Combin. Probab. Comput. 22 (2013), no. 6, 801-828
arxiv created 2012/02/20 · openalex publication_date 2013/09/04 · arxiv updated 2014/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The tensor product ( G 1 , G 2 ) of a graph G 1 and a pointed graph G 2 (containing one distinguished edge) is obtained by identifying each edge of G 1 with the distinguished edge of a separate copy of G 2 , and then removing the identified edges. A formula to compute the Tutte polynomial of a tensor product of graphs was originally given by Brylawski. This formula was recently generalized to coloured graphs and the generalized Tutte polynomial introduced by Bollobás and Riordan. In this paper we generalize the coloured tensor product formula to relative Tutte polynomials of relative graphs, containing zero edges to which the usual deletion/contraction rules do not apply. As we have shown in a recent paper, relative Tutte polynomials may be used to compute the Jones polynomial of a virtual knot.