5 papers
On the determinant of checkerboard colorable virtual knots
Tomoaki Hatano, Yuta Nozaki
For classical knots, Murasugi showed that the determinant modulo is classified by the Arf invariant. Boden and Karimi introduced a determinant for checkerboard colorable virtua…
The Kontsevich invariant and the action of the Grothendieck--Teichmüller group on -component string links
Hisatoshi Kodani, Yuta Nozaki
The Kontsevich invariant of links is independent of the choice of associator, whereas for tangles this is not the case in general. In this paper, we focus on -component string l…
Homotopy types of Hom complexes of graph homomorphisms whose codomains are square-free
Soichiro Fujii, Kei Kimura, Yuta Nozaki
Given finite simple graphs and , the Hom complex is a polyhedral complex having the graph homomorphisms as the vertices. We determine the homoto…
Homotopy types of Hom complexes of graph homomorphisms whose codomains are cycles
Soichiro Fujii, Yuni Iwamasa, Kei Kimura +2
For simple graphs and , the Hom complex is a polyhedral complex whose vertices are the graph homomorphisms and whose edges connect the pairs of…
Colouring normal quadrangulations of projective spaces
Tomáš Kaiser, On-Hei Solomon Lo, Atsuhiro Nakamoto +2
Youngs proved that every non-bipartite quadrangulation of the projective plane is 4-chromatic. Kaiser and Stehl\'ık [J. Combin. Theory Ser. B 113 (2015),…