A note on kernel-perfect orientations and DP-colorings from derangement assignments

TL;DR

This paper generalizes a key lemma to DP-colorings from derangement assignments, leading to new orientation theorems for zero-free signed list colorings, broadening understanding in graph coloring theory.

Contribution

It introduces a generalization of the Bondy-Bopanna-Siegel Lemma to derangement assignments in DP-colorings, extending existing coloring theorems.

Findings

Generalized the Bondy-Bopanna-Siegel Lemma to derangement assignments

Established orientation theorems for zero-free signed list colorings

Connected DP-colorings with derangement assignments to broader graph coloring concepts

Abstract

We prove a generalization of the well-known Bondy-Bopanna-Siegel Lemma to DP-colorings from a class of correspondence assignments which we call derangement assignments. Since DP-colorings from derangement assignments generalize zero-free list colorings of signed graphs, this yields an orientation theorem for zero-free signed list colorings, as well.