Abstract
We investigate the following problem: Given integers m and n, find an acyclic directed graph with m edges and n vertices and two distinguished vertices s and t such that the number of distinct paths from s to t (not necessarily disjoint) is maximized. It is shown that there exists such a graph containing a Hamiltonian path, and its structure is investigated. We give a complete solution to the cases (i) m≤2n-3 and (ii) m = kn- 1 2k(k+1)+r for k =1, 2, ..., n- and r=0,1,2.
| Original language | English |
|---|---|
| Pages (from-to) | 237-245 |
| Number of pages | 9 |
| Journal | Discrete Mathematics |
| Volume | 28 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1979 |
| Externally published | Yes |
Bibliographical note
Funding Information:* The research for this work was carried out while the first author was a visitor at the Weizmann Institute of Science, Rehovot, Israel, and was partially supported by DOE Contract EY-76-C-02-3077. It was concluded at the Courant Institute under NSF Grant MCS-78-03820. ** This work was partially supported by NSF Grant MCS-73-03408 while the second author was a visitor at the University of Illinois.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics