Edgeless graphs are the only universal fixers
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 833-843
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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.
@article{10_1007_s10587_014_0136_3,
author = {Wash, Kirsti},
title = {Edgeless graphs are the only universal fixers},
journal = {Czechoslovak Mathematical Journal},
pages = {833--843},
publisher = {mathdoc},
volume = {64},
number = {3},
year = {2014},
doi = {10.1007/s10587-014-0136-3},
mrnumber = {3298564},
zbl = {06391529},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0136-3/}
}
TY - JOUR AU - Wash, Kirsti TI - Edgeless graphs are the only universal fixers JO - Czechoslovak Mathematical Journal PY - 2014 SP - 833 EP - 843 VL - 64 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0136-3/ DO - 10.1007/s10587-014-0136-3 LA - en ID - 10_1007_s10587_014_0136_3 ER -
Wash, Kirsti. Edgeless graphs are the only universal fixers. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 833-843. doi: 10.1007/s10587-014-0136-3
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