2011/12/07 by Rajai Nasser, Nasser, Rajai
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics #Graph Labeling and Dimension Problems #math.CO
paper · pdf · doi:10.48550/arxiv.1112.1545
25 pages, Master thesis in Graph Theory at the Lebanese University
arxiv created 2011/12/07 · openalex publication_date 2011/12/07 · arxiv updated 2011/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.