When is a poset isomorphic to the poset of connected induced subgraphs of a graph (1996)

by André E Kézdy, Steve Seif
Venue:Southwest J. Pure Appl. Math
Add To MetaCart
Results 1 - 1 of 1

A CHARACTERIZATION OF LATTICE-ORDERED GRAPHS

by David Leach, Matt Walsh - INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7(2) (2007), #A22 , 2007
"... A finite simple graph G is said to be lattice-ordered if the poset of unlabeled induced subgraphs of G, ordered by inclusion, is lattice-ordered. In this paper, we prove that a graph is lattice-ordered if and only if it or its complement is complete multipartite. Furthermore, if two lattice-ordered ..."
Abstract - Add to MetaCart
A finite simple graph G is said to be lattice-ordered if the poset of unlabeled induced subgraphs of G, ordered by inclusion, is lattice-ordered. In this paper, we prove that a graph is lattice-ordered if and only if it or its complement is complete multipartite. Furthermore, if two lattice-ordered graphs have isomorphic unlabeled induced subgraph lattices, then one can be obtained from the other via conjugations and complementations.