Now showing items 1-5 of 5

  • Almost every tree with m edges decomposes K2m,2m 

    Drmota, Michael; Lladó Sánchez, Ana M. (2014-01)
    Article
    Open Access
    We show that asymptotically almost surely a tree with m edges decomposes the complete bipartite graph K2m,2m, a result connected to a conjecture of Graham and Häggkvist. The result also implies that asymptotically almost ...
  • Asymptotic study of subcritical graph classes 

    Drmota, Michael; Fusy, Éric; Kang, Mihyun; Kraus, Veronika; Rué Perna, Juan José (2011-12-01)
    Article
    Open Access
    We present a unified general method for the asymptotic study of graphs from the so-called subcritical graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general ...
  • Maximal independent sets and maximal matchings in series-parallel and related graph classes 

    Drmota, Michael; Ramos, Lander; Requilé, Clément; Rué Perna, Juan José (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
    Conference lecture
    Open Access
    We provide combinatorial decompositions as well as asymptotic tight estimates for two maximal parameters: the number and average size of maximal independent sets and maximal matchings in seriesparallel graphs (and related ...
  • Subgraph statistics in subcritical graph classes 

    Drmota, Michael; Ramos Garrido, Lander; Rué Perna, Juan José (2017-04-01)
    Article
    Open Access
    Let H be a fixed graph and math formula a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in math formula of order n, chosen uniformly at random, follows a ...
  • The Maximum degree of series-parallel graphs 

    Drmota, Michael; Giménez Llach, Omer; Noy Serrano, Marcos (2011-07)
    Article
    Restricted access - confidentiality agreement
    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 ...