We discuss the definability of finite graphs in first-order logic with two relation symbols for adjacency and equality of vertices. The logical depth D(G) of a graph G is equal to ...
In recent results the complexity of isomorphism testing on graphs of bounded treewidth is improved to TC1 [GV06] and further to LogCFL [DTW10]. The computation of canonical forms ...
Let F be a 2-factorization of the complete graph Kv admitting an automorphism group G acting primitively on the set of vertices. If F consists of Hamiltonian cycles, then F is the...
The cone ˆG of a finite graph G is obtained by adding a new vertex p, called the cone point, and joining each vertex of G to p by a simple edge. We show that the rank of the red...
ions (Extended Abstract) Noga Alon Paul Seymour Robin Thomas Let G be an n-vertex graph with nonnegative weights whose sum is 1 assigned to its vertices, and with no minor isomorp...