In the symmetric group on a set of size 2n, let P2n denote the conjugacy class of involutions with no fixed points (equivalently, we refer to these as “pairings”, since each ...
A graph of order n is said to be pancyclic if it contains cycles of all lengths from three to n. Let G be a hamiltonian graph and let x and y be vertices of G that are consecutive ...
Michael Ferrara, Michael S. Jacobson, Angela Harri...
: For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G...
T. C. Edwin Cheng, Yaojun Chen, Yunqing Zhang, C. ...
A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the n...
We shall prove that for all 3 and > 0 there exists a sparse oriented graph of arbitrarily large order with oriented girth and such that any 1/2 + proportion of its arcs induc...