## Facet colouring of nestohedra

##### Abstract

A proper colouring of a polytope is a surjective function from the set of facetsto a set ofmcolours such that every two facets associated with the same colour areseparated, i.e. have no vertex in common. The chromatic number of a polytope is theminimalmsuch that there exists a proper colouring of its facets inmcolours. Thistalk presents the chromatic numbers of associahedra and some others interestingmembers of the family of nestohedra.

##### Keywords:

Hromatic number / Facet colouring / Associahedron / Cyclohedron

##### Source:

Mathematical Meeting of Serbia and Montenegro 2019, 2019, 5-5##### Publisher:

- Faculty of Natural Sciences and Mathematics in Podgorica
- Mathematical Institute of the Serbian Academy of Sciences and Arts
- Faculty of Mathematics in Belgrade
- Matica srpska - Association of Members in Montenegro
- Mathematical Forum of Montenegro

##### Institution

Arhitektonski fakultetTY - CONF AU - Baralić, Djordje AU - Petrić, Zoran AU - Ivanović, Jelena AU - Telebaković Onić, Sonja PY - 2019 UR - https://raf.arh.bg.ac.rs/handle/123456789/1174 AB - A proper colouring of a polytope is a surjective function from the set of facetsto a set ofmcolours such that every two facets associated with the same colour areseparated, i.e. have no vertex in common. The chromatic number of a polytope is theminimalmsuch that there exists a proper colouring of its facets inmcolours. Thistalk presents the chromatic numbers of associahedra and some others interestingmembers of the family of nestohedra. PB - Faculty of Natural Sciences and Mathematics in Podgorica PB - Mathematical Institute of the Serbian Academy of Sciences and Arts PB - Faculty of Mathematics in Belgrade PB - Matica srpska - Association of Members in Montenegro PB - Mathematical Forum of Montenegro C3 - Mathematical Meeting of Serbia and Montenegro 2019 T1 - Facet colouring of nestohedra SP - 5 EP - 5 ER -

@conference{ author = "Baralić, Djordje and Petrić, Zoran and Ivanović, Jelena and Telebaković Onić, Sonja", year = "2019", url = "https://raf.arh.bg.ac.rs/handle/123456789/1174", abstract = "A proper colouring of a polytope is a surjective function from the set of facetsto a set ofmcolours such that every two facets associated with the same colour areseparated, i.e. have no vertex in common. The chromatic number of a polytope is theminimalmsuch that there exists a proper colouring of its facets inmcolours. Thistalk presents the chromatic numbers of associahedra and some others interestingmembers of the family of nestohedra.", publisher = "Faculty of Natural Sciences and Mathematics in Podgorica, Mathematical Institute of the Serbian Academy of Sciences and Arts, Faculty of Mathematics in Belgrade, Matica srpska - Association of Members in Montenegro, Mathematical Forum of Montenegro", journal = "Mathematical Meeting of Serbia and Montenegro 2019", title = "Facet colouring of nestohedra", pages = "5-5" }

Baralić D, Petrić Z, Ivanović J, Telebaković Onić S. Facet colouring of nestohedra. Mathematical Meeting of Serbia and Montenegro 2019. 2019;:5-5

Baralić, D., Petrić, Z., Ivanović, J.,& Telebaković Onić, S. (2019). Facet colouring of nestohedra. Mathematical Meeting of Serbia and Montenegro 2019Mathematical Forum of Montenegro., 5-5.

Baralić Djordje, Petrić Zoran, Ivanović Jelena, Telebaković Onić Sonja, "Facet colouring of nestohedra" (2019):5-5