Vertex Colorings without Rainbow or Monochromatic Subgraphs

TL;DR

This paper explores vertex colorings of graphs that avoid certain rainbow and monochromatic subgraphs, extending previous work by considering more general cases, including the case where the monochromatic subgraph is an edge.

Contribution

It generalizes the study of forbidden rainbow and monochromatic subgraphs in vertex colorings, especially focusing on the case where the monochromatic subgraph is an edge.

Findings

Characterization of colorings avoiding specific rainbow and monochromatic subgraphs

Extension of known results to more general subgraph pairs

New bounds and conditions for forbidden configurations

Abstract

This paper investigates vertex colorings of graphs such that some rainbow subgraph~$R$ and some monochromatic subgraph $M$ are forbidden. Previous work focussed on the case that $R=M$. Here we consider the more general case, especially the case that $M=K_2$.