Aseem Dalal

collaborators

2 papers

math.CO2024

A reduction of the "cycles plus $K_{4}$ 's" problem

Aseem Dalal, Jessica McDonald, Songling Shan

Let $H$ be a 2-regular graph and let $G$ be obtained from $H$ by gluing in vertex-disjoint copies of $K_{4}$ . The "cycles plus $K_{4}$ 's" problem is to show that $G$ is 4-colourable; t…

math.CO2024

Total coloring graphs with large maximum degree

Aseem Dalal, Jessica McDonald, Songling Shan

We prove that for any graph $G$ , the total chromatic number of $G$ is at most $I^ (G) + 2 ⌈ \frac{∣ V ( G ) ∣}{I ^ ( G ) + 1} ⌉$ . This saves one color in comparison with a re…

A reduction of the "cycles plus K4​'s" problem

Total coloring graphs with large maximum degree

A reduction of the "cycles plus $K_{4}$ 's" problem