Search 205,615,552 papers from all fields of science

Search

Sign InCreate Free Account

Corpus ID: 208248424

Kempe Chains and Rooted Minors

@article{Kriesell2019KempeCA,
title={Kempe Chains and Rooted Minors},
author={Matthias Kriesell and Samuel Mohr},
journal={arXiv: Combinatorics},
year={2019}
}

A (minimal) transversal of a partition is a set which contains exactly one element from each member of the partition and nothing else. A coloring of a graph is a partition of its vertex set into anticliques, that is, sets of pairwise nonadjacent vertices. We study the following problem: Given a transversal $T$ of a proper coloring $\mathfrak{C}$ of some graph $G$, is there a partition $\mathfrak{H}$ of a subset of $V(G)$ into connected sets such that $T$ is a transversal of $\mathfrak{H}$ and… Expand

It is proved that if G has no antitriangles and G has exactly one c(G)-coloring then s(G) is at least |V(G)|/2, where the proof does not use the four-color-theorem.Expand

This book provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal, and is suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science.Expand