Let G be a simple graph with maximum degree Δ(G). A subgraph H of is overfull if |E(H)|>Δ(G)⌊|V(H)|/2⌋. Chetwynd and Hilton in 1986 conjectured that on n vertices Δ(G)>n/3 has chromatic index Δ(G) only contains no subgraph. Glock, Kühn Osthus 2016 showed the conjecture true for dense quasirandom graphs even order, they same should hold such odd order. In this paper, we show affirmative.

We investigate the effect of a fixed forbidden clique minor upon strong chromatic index, both in multigraphs and simple graphs. conjecture for each k ? 4 that any K -minor-free multigraph maximum degree ? has index at most 3 2 ( ? ) ?. present construction certifying if true is asymptotically sharp as ? ?. In support conjecture, we show it case = prove statement number place index. By contrast,...

An acyclic edge coloring of a graph is proper in which there are no bichromatic cycles. The chromatic index $G$ denoted by $a'(G)$, the minimum positive integer $k$ such that has an with colors. It been conjectured Fiam\v{c}\'{\i}k $a'(G) \le \Delta+2$ for any maximum degree $\Delta$. Linear arboricity $G$, $la(G)$, number linear forests into edges can be partitioned. A said to chordless if cyc...

A strong edge coloring of a graph G is a proper edge coloring in which every color class is an induced matching. The strong chromatic index χs(G) of a graph G is the minimum number of colors in a strong edge coloring of G. In this note, we improve a result by Dębski et al. [Strong chromatic index of sparse graphs, arXiv:1301.1992v1] and show that the strong chromatic index of a k-degenerate gra...