The Existence of Semi-colorings in a Graph

A semi-coloring is a fractional-type edge coloring of graphs. Daniely and Linial (J Graph Theory 69:426–440, 2012) conjectured that every graph has a semi-coloring. In this paper, we give an affirmative answer to this conjecture by considering a 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-factor in almost regular graphs.