Triangle-different Hamiltonian paths

István Kovács; Dániel Soltész

Triangle-different Hamiltonian paths

Combinatorics 2016-10-13 v2

Authors: István Kovács , Dániel Soltész

Abstract

Let $G$ be a fixed graph. Two paths of length $n-1$ on $n$ vertices (Hamiltonian paths) are $G$ -different if there is a subgraph isomorphic to $G$ in their union. In this paper we prove that the maximal number of pairwise triangle-different Hamiltonian paths is equal to the number of balanced bipartitions of the ground set, answering a question of K\"orner, Messuti and Simonyi.

Keywords

hamilton cycles dyck paths graph theory

Cite

@article{arxiv.1608.05237,
  title  = {Triangle-different Hamiltonian paths},
  author = {István Kovács and Dániel Soltész},
  journal= {arXiv preprint arXiv:1608.05237},
  year   = {2016}
}

Comments

We slightly changed the introduction, added two more papers as references, and added a new short section which deals with the two related questions where Hamiltonian paths are replaced with arbitrary graphs and trees

Triangle-different Hamiltonian paths

Abstract

Keywords

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