Reducing Vizing’s 2-Factor Conjecture to Meredith Extension of Critical Graphs

• Published in: Graphs and combinatorics Vol. 36; no. 5; pp. 1585 - 1591
• Main Authors: Chen, Xiaodong, Ji, Qing, Liu, Mingda
• Format: Journal Article
• Language: English
• Published: Tokyo Springer Japan 01.09.2020; Springer Nature B.V
• Subjects: Combinatorics; Engineering Design; Graph theory; Graphs; Mathematics; Mathematics and Statistics; Original Paper; 68R10; Grünewald and Steffen construction; 2-Factor; Critical and almost regular graphs; Independence number

A simple graph G is called Δ - critical if χ ′ ( G ) = Δ ( G ) + 1 and χ ′ ( H ) ≤ Δ ( G ) for every proper subgraph H of G , where Δ ( G ) and χ ′ ( G ) are the maximum degree and the chromatic index of G , respectively. Vizing in 1965 conjectured that any Δ -critical graph contains a 2-factor, whi...