• Homomorphisms between graphs embedded in surfaces 

      Garijo Royo, Delia; Goodall, Andrew; Vena Cros, Lluís (Elsevier, 2024-05)
      Article
      Accés obert
      We extend the notion of graph homomorphism to cellularly embedded graphs (maps) by designing operations on vertices and edges that respect the surface topology; we thus obtain the first definition of map homomorphism that ...
    • Irreducibility of the Tutte polynomial of an embedded graph 

      Ellis Monaghan, Joanna A.; Goodall, Andrew; Moffatt, Iain; Noble, Steven D.; Vena Cros, Lluís (2022-12-19)
      Article
      Accés obert
      We prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous ...
    • On the evaluation of the Tutte polynomial at the points (1,-1) and (2,-1) 

      Goodall, Andrew; Merino, Criel; Mier Vinué, Anna de; Noy Serrano, Marcos (2010)
      Text en actes de congrés
      Accés obert
      C. Merino proved recently the following identity between evaluations of the Tutte polynomial of complete graphs: t($K_{n+2}$; 1,−1) = t($K_n$;2,−1). In this work we extend this result by giving a large class of graphs with ...
    • The canonical Tutte polynomial for signed graphs 

      Goodall, Andrew; Litjens, Bart; Regts, Guus; Vena Cros, Lluís (2019)
      Text en actes de congrés
      Accés obert
      We construct a new polynomial invariant for signed graphs, the trivariate Tutte polynomial, which contains among its evaluations the number of proper colorings and the number of nowhere-zero flows. In this, it parallels ...
    • The Tutte polynomial characterizes simple outerplanar graphs 

      Goodall, Andrew; Mier Vinué, Anna de; Noble, S.; Noy Serrano, Marcos (2011-07)
      Article
      Accés restringit per acord de confidencialitat
      We show that if G is a simple outerplanar graph and H is a graph with the same Tutte polynomial as G, then H is also outerplanar. Examples show that the condition of G being simple cannot be omitted.