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- Centre National de la Recherche ScientifiqueFR17 papers
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24 papers · 1 filter
Incidence Hypergraphs: Injectivity, Uniformity, and Matrix-tree Theorems
Will Grilliette, Josephine Reynes, Lucas J. Rusnak
An oriented hypergraph is an oriented incidence structure that allows for the generalization of graph theoretic concepts to integer matrices through its locally signed graphic subs…
Algebraic algorithms for even circuits in graphs
Huy Tai Ha, Susan Morey
We present an algebraic algorithm to detect the existence of and to list all indecomposable even circuits in a given graph. We also discuss an application of our work to the study…
Steinberg's theorem for crystallographic complex reflection groups
Philip Puente, Anne V. Shepler
Popov classified crystallographic complex reflection groups by determining lattices they stabilize. These analogs of affine Weyl groups have infinite order and are generated by ref…
The zero forcing polynomial of a graph
Kirk Boyer, Boris Brimkov, Sean English +5
Zero forcing is an iterative graph coloring process, where given a set of initially colored vertices, a colored vertex with a single uncolored neighbor causes that neighbor to beco…
Chorded pancyclicity in -partite graphs
Daniela Ferrero, Linda Lesniak
We prove that for any integers and any -tuple of positive integers such that and , th…
Oriented Hypergraphic Matrix-tree Type Theorems and Bidirected Minors via Boolean Order Ideals
Ellen Robinson, Lucas J. Rusnak, Martin Schmidt +1
Restrictions of incidence-preserving path maps produce an oriented hypergraphic All Minors Matrix-tree Theorems for Laplacian and adjacency matrices. The images of these maps produ…