# Disproving the normal graph conjecture

Abstract : A graph $G$ is called normal if there exist two coverings, $\mathbb{C}$ and $\mathbb{S}$ of its vertex set such that every member of $\mathbb{C}$ induces a clique in $G$, every member of $\mathbb{S}$ induces an independent set in $G$ and $C \cap S \neq \emptyset$ for every $C \in \mathbb{C}$ and $S \in \mathbb{S}$. It has been conjectured by De Simone and K\"orner in 1999 that a graph $G$ is normal if $G$ does not contain $C_5$, $C_7$ and $\overline{C_7}$ as an induced subgraph. We disprove this conjecture.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-01982435
Contributor : Lucas Pastor <>
Submitted on : Tuesday, January 15, 2019 - 4:24:17 PM
Last modification on : Monday, January 20, 2020 - 12:14:06 PM

### Identifiers

• HAL Id : hal-01982435, version 1
• ARXIV : 1508.05487

### Citation

Ararat Harutyunyan, Lucas Pastor, Stéphan Thomassé. Disproving the normal graph conjecture. 2019. ⟨hal-01982435⟩

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