Generalized fibonacci maximum path graphs

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)237-245
Number of pages9
JournalDiscrete Mathematics
Issue number3
StatePublished - 1979
Externally publishedYes

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


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