𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Topology of bounded-degree graph complexes

✍ Scribed by Xun Dong

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
254 KB
Volume
262
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

The bounded-degree graph complexes were first introduced by Reiner and Roberts [J. Algebraic Combin. 11 (2000) 135-154]. They arise from the finite free resolution of quadratic Veronese rings and modules. We prove various results about the homotopy types of these complexes, and deduce corresponding characteristic-free results about the quadratic Veronese resolutions. In particular, we characterize the set of multidegrees which support at least one higher syzygy in this resolution. The answer turns out to be independent of the field characteristic.

πŸ“œ SIMILAR VOLUMES

Matching Complexes, Bounded Degree Graph
Matching Complexes, Bounded Degree Graph Complexes, and Weight Spaces of GLn-Complexes
✍ Dikran B. Karaguezian; Victor Reiner; Michelle L. Wachs πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 124 KB

We present a technique for lifting results on the homology of matching complexes of certain types of graphs and hypergraphs to general bounded degree graph complexes. This technique is based on our observation that homological results of Bouc on matching complexes, of Reiner and Roberts on bounded d

Judicious partitions of bounded-degree g
Judicious partitions of bounded-degree graphs
✍ B. BollobΓ‘s; A. D. Scott πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 118 KB πŸ‘ 1 views

## Abstract We prove results on partitioning graphs __G__ with bounded maximum degree. In particular, we provide optimal bounds for bipartitions __V__(__G__) = __V__~1~ βˆͺ __V__~2~ in which we minimize {__e__(__V__~1~), __e__(__V__~2~)}. Β© 2004 Wiley Periodicals, Inc. J Graph Theory 46: 131–143, 200

Packing triangles in bounded degree grap
Packing triangles in bounded degree graphs
✍ Alberto Caprara; Romeo Rizzi πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 103 KB

We consider the two problems of finding the maximum number of node disjoint triangles and edge disjoint triangles in an undirected graph. We show that the first (respectively second) problem is polynomially solvable if the maximum degree of the input graph is at most 3 (respectively 4), whereas it i

Decreasing the diameter of bounded degre
Decreasing the diameter of bounded degree graphs
✍ Noga Alon; AndrΓ‘s GyΓ‘rfΓ‘s; MiklΓ³s RuszinkΓ³ πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 118 KB πŸ‘ 2 views
Polychromatic colorings of bounded degre
Polychromatic colorings of bounded degree plane graphs
✍ Elad Horev; Roi Krakovski πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 289 KB

## Abstract A __polychromatic k__‐__coloring__ of a plane graph __G__ is an assignment of __k__ colors to the vertices of __G__ such that every face of __G__ has __all k__ colors on its boundary. For a given plane graph __G__, one seeks the __maximum__ number __k__ such that __G__ admits a polychro