The hypermetric cone and polytope on eight vertices and some generalizations

Deza, Michel; Sikirić, Mathieu Dutour

doi:10.1016/j.jsc.2016.01.009

Cited by 4 publications

(4 citation statements)

References 36 publications

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“…The hypermetric cone is interpreted in term of parameter space of Delaunay polytopes and this viewpoint was introduced first in [3]. A complete description of the facets of the hypermetric cone was achieved in [4] for = 6, [5,20,7] for = 7 and [8].…”

Section: Introductionmentioning

confidence: 99%

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Гиперметрический Конус И Многогранник На Графах

Дютур-Сикирич¹

2019

Chebyshevskii Sbornik

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Section: Introductionmentioning

confidence: 99%

“…, } 2 → R, such that ( , ) ≤ ( + 1) is satisfied for all ∈ Z with ∑︀ = 1 + 2 and ∈ Z. It was defined in [8,15] and it is related to centrally symmetric Delaunay polytopes (see 2.2 for some summary).…”

Section: Introductionmentioning

confidence: 99%

Гиперметрический Конус И Многогранник На Графах

Дютур-Сикирич¹

2019

Chebyshevskii Sbornik

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Section: Introductionmentioning

confidence: 99%

The hypermetric cone and polytope on graphs

Dutour

2019

Chebyshevskii Sbornik

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Гиперметрический конус был определен в [9] и был широко изучен Мишелем Дезой и его сотрудниками. Еще одним ключевым его интересом был отрезной и метрический многогранник, который он рассматривал в своих последних работах в случае графов.Здесь мы объединяем оба интереса, рассматривая гиперметрию на графах. Мы определяем их для любого графа и даем алгоритм вычисления экстремальных лучей и граней гиперметрического конуса на графах. Мы вычисляем гиперметрический конус для первого нетривиального случая 7 − { }. Мы также вычисляем гиперметрический конус в случае графов без 5 минора.Ключевые слова: алгебраические решётки, алгебраические сетки, тригонометрические суммы алгебраических сеток с весами, весовые функции.Библиография: 21 название.

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“…Besides further studies of the existing cones and the ones defined in this paper, two other cases could be interesting. One is to extend the notion of hypermetrics cone HYP(K n ) to graphs; several approaches were considered in [18], for example projecting only on the relevant coordinates, but no general results were proved.…”

Section: Introductionmentioning

confidence: 99%

Generalized cut and metric polytopes of graphs and simplicial complexes

Deza¹,

Sikirić

2018

Optim Lett

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Given a graph G one can define the cut polytope CUTP(G) and the metric polytope METP(G) of this graph and those polytopes encode in a nice way the metric on the graph. According to Seymour's theorem, CUTP(G) = METP(G) if and only if K 5 is not a minor of G.We consider possibly extensions of this framework: (1) We compute the CUTP(G) and METP(G) for many graphs.(2) We define the oriented cut polytope WOMCUTP(G) and oriented multicut polytope OMCUTP(G) as well as their oriented metric version QMETP(G) and WQMETP(G). (3) We define an n-dimensional generalization of metric on simplicial complexes.

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The hypermetric cone and polytope on eight vertices and some generalizations

Cited by 4 publications

References 36 publications

Гиперметрический Конус И Многогранник На Графах

Гиперметрический Конус И Многогранник На Графах

The hypermetric cone and polytope on graphs

Generalized cut and metric polytopes of graphs and simplicial complexes

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