Title

Paths in graphs

Abstract

We prove that if 10 ≦ (k2) ≦ m < (k+12) then the number of paths of length three in a graph G of size m is at most 2m(m - k)(k - 2)/k. Equality is attained iff G is the union of Kk and isolated vertices. We also give asymptotically best possible bounds for the maximal number of paths of length s, for arbitrary s, in graphs of size m. Lastly, we discuss the more general problem of maximizing the number of subgraphs isomorphic to a given graph H in graphs of size m.

Publication Title

Studia Scientiarum Mathematicarum Hungarica

Share

COinS