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http://dx.doi.org/10.5831/HMJ.2014.36.1.85

GRAPHICAL ARRANGEMENTS OF COMPRESSED GRAPHS

Nguyen, Thi A. (Department of Mathematics, Chonnam National University)
Kim, Sangwook (Department of Mathematics, Chonnam National University)

Publication Information

Honam Mathematical Journal / v.36, no.1, 2014 , pp. 85-102 More about this Journal

Abstract

We show that if a graph G is compressed, then the proper part of the intersection poset of the corresponding graphical arrangement $A_G$ has the homotopy type of a wedge of spheres. Furthermore, we also indicate the number of spheres in the wedge, based on the number of adjacent edges of vertices in G.

Keywords

compressed graph; graphical arrangement;

Citations & Related Records

Reference

1	Anders Bjorner, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc., 260(1) (1980), 159-183. DOI
2	Anders Bjorner and Michelle Wachs, On lexicographically shellable posets, Trans. Amer. Math. Soc., 277(1) (1983), 323-341. DOI
3	Anders Bjorner and Michelle L. Wachs, Shellable nonpure complexes and posets. I, Trans. Amer. Math. Soc., 348(4) (1996), 1299-1327. DOI
4	Peter Orlik and Louis Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math., 56(2) (1980), 167-189. DOI
5	Anders Bjorner and Michelle L. Wachs, Shellable nonpure complexes and posets. II, Trans. Amer. Math. Soc., 349(10) (1997), 3945-3975. DOI
6	Curtis Greene and Thomas Zaslavsky, On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs, Trans. Amer. Math. Soc., 280(1) (1983), 97-126. DOI ScienceOn
7	Dmitry Kozlov, Combinatorial algebraic topology, volume 21 of Algorithms and Computation in Mathematics, Springer, Berlin, 2008.
8	R. P. Stanley, Supersolvable lattices, Algebra Universalis, 2 (1972), 197-217. DOI
9	Richard P. Stanley, An introduction to hyperplane arrangements, In Geometric combinatorics, volume 13 of IAS/Park City Math. Ser., pages 389-496. Amer. Math. Soc., Providence, RI, 2007.
10	Michelle L. Wachs, A basis for the homology of the d-divisible partition lattice, Adv. Math., 117(2) (1996), 294-318. DOI ScienceOn
11	Michelle L. Wachs, Poset topology: tools and applications, In Geometric combinatorics, volume 13 of IAS/Park City Math. Ser., pages 497-615. Amer. Math. Soc., Providence, RI, 2007.
12	Thomas Zaslavsky, Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc., 1(issue 1, 154):vii+102, 1975.
13	Peter Orlik and Hiroaki Terao, Arrangements of hyperplanes, volume 300 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 1992.