Graphs on Graphs

Comparability graphs and cover-incomparability graphs (C-I graphs) are two interesting classes of graphs from posets. Comparability graph of a poset $P=(V,\le )$ is a graph with vertex set V and two vertices u and v are adjacent in V if u and v are ...

Thomassen conjectured that every 4-connected line graph is Hamiltonian. Chen and Lai [Z.-H. Chen, H.-J. Lai, Reduction techniques for super-Eulerian graphs and related topics-an update, in: Ku Tung-Hsin (Ed.), Combinatorics and Graph Theory, vol. 95, ...

A graph G is equimatchable if each matching in G is a subset of a maximum-size matching and it is factor critical if G-v has a perfect matching for each vertex v of G. It is known that any 2-connected equimatchable graph is either bipartite or factor ...