English

Oriented paths in n-chromatic digraphs

Combinatorics 2011-12-08 v1

Abstract

In this thesis, we try to treat the problem of oriented paths in n-chromatic digraphs. We first treat the case of antidirected paths in 5-chromatic digraphs, where we explain El-Sahili's theorem and provide an elementary and shorter proof of it. We then treat the case of paths with two blocks in n-chromatic digraphs with n greater than 4, where we explain the two different approaches of Addario-Berry et al. and of El-Sahili. We indicate a mistake in Addario-Berry et al.'s proof and provide a correction for it.

Cite

@article{arxiv.1112.1545,
  title  = {Oriented paths in n-chromatic digraphs},
  author = {Rajai Nasser},
  journal= {arXiv preprint arXiv:1112.1545},
  year   = {2011}
}

Comments

25 pages, Master thesis in Graph Theory at the Lebanese University

R2 v1 2026-06-21T19:47:45.227Z