#### Volume 8, issue 4 (2008)

 Download this article For screen For printing
 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Marked tubes and the graph multiplihedron

### Satyan Devadoss and Stefan Forcey

Algebraic & Geometric Topology 8 (2008) 2081–2108
##### Abstract

Given a graph $G$, we construct a convex polytope whose face poset is based on marked subgraphs of $G$. Dubbed the graph multiplihedron, we provide a realization using integer coordinates. Not only does this yield a natural generalization of the multiplihedron, but features of this polytope appear in works related to quilted disks, bordered Riemann surfaces and operadic structures. Certain examples of graph multiplihedra are related to Minkowski sums of simplices and cubes and others to the permutohedron.

##### Keywords
multiplihedron, graph associahedron, realization, convex hull
##### Mathematical Subject Classification 2000
Primary: 52B11
Secondary: 18D50, 55P48
##### Publication
Received: 28 July 2008
Revised: 10 October 2008
Accepted: 13 October 2008
Published: 12 November 2008
##### Authors
 Satyan Devadoss Department of Mathematics and Statistics Williams College Williamstown, MA 01267 USA http://www.williams.edu/mathematics/devadoss/ Stefan Forcey Department of Physics and Mathematics Tennessee State University Nashville, TN 37209 USA http://faculty.tnstate.edu/sforcey/