• 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 ...
    • Normal limiting distributions for systems of linear equations in random sets 

      Rué Perna, Juan José; Wotzel, Maximilian (Elsevier, 2022-09-15)
      Article
      Accés obert
      We consider the binomial random set model where each element in is chosen independently with probability . We show that for essentially all regimes of p and very general conditions for a matrix A and a column vector b, the ...
    • The Maximum degree of series-parallel graphs 

      Drmota, Michael; Giménez Llach, Omer; Noy Serrano, Marcos (2011-07)
      Article
      Accés restringit per acord de confidencialitat
      We prove that the maximum degree Δn of a random series-parallel graph with n vertices satisfies Δn/ log n → c in probability, and EΔn ∼ c log n for a computable constant c > 0. The same kind of result holds for 2-connected ...