2020/04/19 by Hiroko Morishita, Morishita, Hiroko, Ryo Nikkuni +1
Computer Science · Mathematics · #57K10 #57M15 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics #Discrete mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Graph #Graph power #Hamiltonian path #Line graph #Mathematics #Wheel graph #math.GT #msc:57K10 #msc:57M15
paper · pdf · doi:10.48550/arxiv.2004.10013
published in arXiv (Cornell University) (Cornell University) · 27 pages, 4 figures. arXiv admin note: text overlap with arXiv:1807.02805
openalex publication_date 2020/04/19 · openalex created_date 2020/05/01 · arxiv created 2021/04/08 · arxiv updated 2021/04/09 · openalex updated_date 2026/08/05
Conway and Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent two-component links is odd, and Kazakov and Korablev proved that for every spatial complete graph with arbitrary number of vertices greater than six, the sum of the linking numbers over all of the constituent two-component Hamiltonian links is even. In this paper, we show that for every spatial complete graph whose number of vertices is greater than six, the sum of the square of the linking numbers over all of the two-component Hamiltonian links is determined explicitly in terms of the sum over all of the triangle-triangle constituent links. As an application, we show that if the number of vertices is sufficiently large then every spatial complete graph contains a two-component Hamiltonian link whose absolute value of the linking number is arbitrary large. Some applications to rectilinear spatial complete graphs are also given.