9 papers
Cops and Robbers: A -homotopy Invariant Variant
Tien Chih, Laura Scull
Cops and Robbers is a pursuit-evasion game played on graphs, of which many variants have been developed and studied. We introduce a variant of this game, "Sneaky-Active Cops and Ro…
Combinatorics of factorization systems on lattices
Jishnu Bose, Tien Chih, Hannah Housden +4
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in…
Fundamental Groups of Hamming Graphs
Keira Behal, Tien Chih
Recently there has been growing interest in discrete homotopies and homotopies of graphs beyond treating graphs as 1-dimensional simplicial spaces. One such type of homotopy is $\t…
Homotopy Covers of Graphs
Tien Chih, Laura Scull
We develop a theory of -homotopy, fundamental groupoids and covering spaces that apply to non-simple graphs, generalizing existing results for simple graphs. We prove that…
Fundamental Groupoids for Graphs
Tien Chih, Laura Scull
In this paper, we develop a -homotopy fundamental groupoid for graphs, and show a functorial relationship to the 2-category of graphs. We further explore the fundamental gr…
A Homotopy Category for Graphs
Tien Chih, Laura Scull
We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in term…
The Fundamental Morphism Theorem in the Categories of Graphs & Graph Reconstruction
Tien Chih, Demitri Plessas
The Fundamental Morphism Theorem is a categorical version of the First Noether Isomorphism Theorem for categories that do not have kernels or cokernels. We consider two categories…
Graphs and Their Associated Inverse Semigroups
Tien Chih, Demitri Plessas
Directed graphs have long been used to gain understanding of the structure of semigroups, and recently the structure of directed graph semigroups has been investigated resulting in…
Generalized Affine Programming & Duality Gap with non-Division Rings
Tien Chih
Classical primal-dual affine programming takes place over finite dimensional real vector spaces. This results in beautiful duality theory, connecting the optimal solu- tions of the…