Generating sequences of clique-symmetric graphs via Eulerian digraphs

Generating sequences of clique-symmetric graphs via Eulerian digraphs

Let {Gp1, Gp2, . . .} be an infinite sequence of graphs with Gpn having pn vertices. This sequence is called Kp-removable if Gp1 ∼= Kp, and Gpn − S ∼= Gp(n−1) for every n ≥ 2 and every vertex subset S of Gpn that induces a Kp. Each graph in such a sequence has a high degree of symmetry: every way of removing the vertices of any fixed number of disjoint Kp’s yields the same subgraph. Here we con...

The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs

Let RT (n), ED(n) and EOG(n) be the number of labelled regular tournaments, labelled loop-free simple Eulerian digraphs, and labelled Eulerian oriented simple graphs, respectively, on n vertices. Then, as n →∞, RT (n) = (2n+1 πn )(n−1)/2 n1/2e−1/2 ( 1 + O(n−1/2+ ) ) (n odd), ED(n) = ( 4 πn )(n−1)/2 n1/2e−1/4 ( 1 + O(n−1/2+ ) ) , and EOG(n) = (3n+1 4πn )(n−1)/2 n1/2e−3/8 ( 1 + O(n−1/2+ ) ) , for...

Vertex Removable Cycles of Graphs and Digraphs

‎In this paper we defined the vertex removable cycle in respect of the following‎, ‎if $F$ is a class of graphs(digraphs)‎ ‎satisfying certain property‎, ‎$G in F $‎, ‎the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $.‎ ‎The vertex removable cycles of eulerian graphs are studied‎. ‎We also characterize the edge removable cycles of regular‎ ‎graphs(digraphs).‎    

Circuits in Graphs and Digraphs via Embeddings

Bounding Clique-Width via Perfect Graphs

Given two graphs H1 and H2, a graph G is (H1,H2)-free if it contains no subgraph isomorphic to H1 or H2. We continue a recent study into the clique-width of (H1,H2)-free graphs and present three new classes of (H1, H2)-free graphs that have bounded clique-width. We also show the implications of our results for the computational complexity of the Colouring problem restricted to (H1,H2)-free grap...