On-line algorithms for ordered sets and comparability graphs

Citations of this article
Mendeley users who have this article in their library.


We discuss several results concerning on-line algorithms for ordered sets and comparability graphs. The main new result is on the problem of on-line transitive orientation. We view on-line transitive orientation of a comparability graph G as a two-person game. In the ith round of play, 1 ≤ i ≤ | V(G)|, player A names a graph Gi such that Gi is isomorphic to a subgraph of G, |V(Gi)| = i, and Gi-1 is an induced subgraph of Gi if i > 1. Player B must respond with a transitive orientation of Gi which extends the transitive orientation given to Gi-1 in the previous round of play. Player A wins if and only if player B fails to give a transitive orientation to Gi for some i, 1 ≤ i ≤ |V(G)|. Our main result shows that player A has at most three winning moves. We also discuss applications to on-line clique covering of comparability graphs, and we mention some open problems. © 1995.




Penrice, S. G. (1995). On-line algorithms for ordered sets and comparability graphs. Discrete Applied Mathematics, 60(1–3), 319–329. https://doi.org/10.1016/0166-218X(94)00062-I

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free