Upper bounds on the odd graceful chromatic number of graphs

TL;DR

This paper establishes new upper bounds for the odd graceful chromatic number of bipartite graphs, relating it to graph size and related chromatic numbers, advancing understanding of graph coloring constraints.

Contribution

It introduces several novel upper bounds for the odd graceful chromatic number of bipartite graphs, some depending solely on vertex count or related chromatic numbers.

Findings

New upper bounds depending on vertex count

Bounds related to chromatic numbers of related graphs

Improved understanding of coloring constraints in bipartite graphs

Abstract

We obtain several new upper bounds of the odd graceful chromatic number of a graph $G$, which must be bipartite. Some of our bounds depend only on the number of the vertices of $G$ or the chromatic number of some graphs related to the bipartition of $G$.