Marked tubes and the graph multiplihedron

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 multiphihedron, 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.

23 pages, 17 figures

References in corpus (3)

• Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an $S^1$-Equivariant Pair
• Geometric realizations of the multiplihedron and its complexification
• A Realization of Graph-Associahedra

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• Shuffles and Concatenations in Constructing of Graphs
• Species substitution, graph suspension, and graded Hopf algebras of painted tree polytopes
• Lifted generalized permutahedra and composition polynomials
• Gromov-Witten Theory of P^1xP^1xP^1
• New Hopf Structures on Binary Trees (Extended Abstract)