12 citations · 39 across the 11 of their papers we have counts for
11 papers
Two-connected graphs with prescribed three-connected components
Andrei Gagarin, Gilbert Labelle, Pierre Leroux +1
We adapt the classical 3-decomposition of any 2-connected graph to the case of simple graphs (no loops or multiple edges). By analogy with the block-cutpoint tree of a connected gr…
Counting unlabelled toroidal graphs with no K33-subdivisions
Andrei Gagarin, Gilbert Labelle, Pierre Leroux
We provide a description of unlabelled enumeration techniques, with complete proofs, for graphs that can be canonically obtained by substituting 2-pole networks for the edges of co…
Characterization and enumeration of toroidal K_{3,3}-subdivision-free graphs
Andrei Gagarin, Gilbert Labelle, Pierre Leroux
We describe the structure of 2-connected non-planar toroidal graphs with no K_{3,3}-subdivisions, using an appropriate substitution of planar networks into the edges of certain gra…
The structure and labelled enumeration of K_{3,3}-subdivision-free projective-planar graphs
Andrei Gagarin, Gilbert Labelle, Pierre Leroux
We consider the class F of 2-connected non-planar K_{3,3}-subdivision-free graphs that are embeddable in the projective plane. We show that these graphs admit a unique decompositio…
Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice
Dominique Gouyou-Beauchamps, Pierre Leroux
Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate the symmetry classes of convex hexagonal polyominoes. Here convexity is to be understood as convexity a…
Enumerative problems inspired by Mayer's theory of cluster integrals
Pierre Leroux
The basic functional equations for connected and 2-connnected graphs can be traced back to the statistical physicists Mayer and Husimi. They play an essential role in establishing…