Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-01982435
Contributor : Lucas Pastor <>
Submitted on : Tuesday, January 15, 2019 - 4:24:17 PM
Last modification on : Friday, April 30, 2021 - 10:03:57 AM

Links full text

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⟩

Share

Metrics

Record views

196