Multi-triangulations as complexes of star polygons

Vincent Pilaud; Francisco Santos

Multi-triangulations as complexes of star polygons

Vincent Pilaud
, Francisco Santos

CSIC-Univ. Cantabria

Research output: Contribution to conference › Paper › peer-review

Abstract

A k-triangulation of a convex polygon is a maximal set of diagonals so that no k+1 of them mutually cross. k-triangulations have received attention in recent literature, with motivation coming from several interpretations of them.We present a new way of looking at k-triangulations, where certain star polygons naturally generalize triangles for k-triangulations. With this tool we give new, direct proofs of the fundamental properties of k-triangulations (number of edges, definition of flip). This interpretation also opens up new avenues of research that we briefly explore in the last section.

Original language	English
Pages	319-330
Number of pages	12
Publication status	Published - 1 Dec 2008
Event	20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile Duration: 23 Jun 2008 → 27 Jun 2008

Conference

Conference	20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08
Country/Territory	Chile
City	Valparaiso
Period	23/06/08 → 27/06/08

Keywords

Crossing-free graph
Generalized triangulation
Star polygon

Cite this

@conference{077788b90a4d490e932045576e6700c6,

title = "Multi-triangulations as complexes of star polygons",

abstract = "A k-triangulation of a convex polygon is a maximal set of diagonals so that no k+1 of them mutually cross. k-triangulations have received attention in recent literature, with motivation coming from several interpretations of them.We present a new way of looking at k-triangulations, where certain star polygons naturally generalize triangles for k-triangulations. With this tool we give new, direct proofs of the fundamental properties of k-triangulations (number of edges, definition of flip). This interpretation also opens up new avenues of research that we briefly explore in the last section.",

keywords = "Crossing-free graph, Generalized triangulation, Star polygon",

author = "Vincent Pilaud and Francisco Santos",

year = "2008",

month = dec,

day = "1",

language = "English",

pages = "319--330",

note = "20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 ; Conference date: 23-06-2008 Through 27-06-2008",

}

TY - CONF

T1 - Multi-triangulations as complexes of star polygons

AU - Pilaud, Vincent

AU - Santos, Francisco

PY - 2008/12/1

Y1 - 2008/12/1

N2 - A k-triangulation of a convex polygon is a maximal set of diagonals so that no k+1 of them mutually cross. k-triangulations have received attention in recent literature, with motivation coming from several interpretations of them.We present a new way of looking at k-triangulations, where certain star polygons naturally generalize triangles for k-triangulations. With this tool we give new, direct proofs of the fundamental properties of k-triangulations (number of edges, definition of flip). This interpretation also opens up new avenues of research that we briefly explore in the last section.

AB - A k-triangulation of a convex polygon is a maximal set of diagonals so that no k+1 of them mutually cross. k-triangulations have received attention in recent literature, with motivation coming from several interpretations of them.We present a new way of looking at k-triangulations, where certain star polygons naturally generalize triangles for k-triangulations. With this tool we give new, direct proofs of the fundamental properties of k-triangulations (number of edges, definition of flip). This interpretation also opens up new avenues of research that we briefly explore in the last section.

KW - Crossing-free graph

KW - Generalized triangulation

KW - Star polygon

M3 - Paper

AN - SCOPUS:84860490542

SP - 319

EP - 330

T2 - 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08

Y2 - 23 June 2008 through 27 June 2008

ER -

Multi-triangulations as complexes of star polygons

Abstract

Conference

Keywords

Fingerprint

Cite this