1. Edgeless graphs are the only universal fixers
- Creator:
- Wash, Kirsti
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- universal fixer and domination
- Language:
- English
- Description:
- Given two disjoint copies of a graph $G$, denoted $G^1$ and $G^2$, and a permutation $\pi $ of $V(G)$, the graph $\pi G$ is constructed by joining $u \in V(G^1)$ to $\pi (u) \in V(G^2)$ for all $u \in V(G^1)$. $G$ is said to be a universal fixer if the domination number of $\pi G$ is equal to the domination number of $G$ for all $\pi $ of $V(G)$. In 1999 it was conjectured that the only universal fixers are the edgeless graphs. Since then, a few partial results have been shown. In this paper, we prove the conjecture completely.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public