4 citations · 6 across the 14 of their papers we have counts for
14 papers
Pattern Forcing (0,1)-Matrices
Lei Cao, Shen-Fu Tsai
We introduce two related notions of pattern enforcement in -matrices: -forcing and strongly -forcing, which formalize distinct ways a fixed pattern must appear wit…
Throttling for metric dimension and its variants
Boris Brimkov, Peter Diao, Jesse Geneson +4
Metric dimension is a graph parameter that has been applied to robot navigation and finding low-dimensional vector embeddings. Throttling entails minimizing the sum of two availabl…
Fault tolerance for metric dimension and its variants
Jesse Geneson, Shen-Fu Tsai
Hernando et al. (2008) introduced the fault-tolerant metric dimension , which is the size of the smallest resolving set of a graph such that $S-\left\{s\ri…
Sequence saturation
Anand, Jesse Geneson, Suchir Kaustav +1
In this paper, we introduce saturation and semisaturation functions of sequences, and we prove a number of fundamental results about these functions. Given a forbidden sequence …
Extremal bounds for pattern avoidance in multidimensional 0-1 matrices
Jesse Geneson, Shen-Fu Tsai
A 0-1 matrix contains another 0-1 matrix if some submatrix of can be turned into by changing any number of -entries to -entries. is -saturate…
Random processes for generating task-dependency graphs
Jesse Geneson, Shen-Fu Tsai
We investigate random processes for generating task-dependency graphs of order with edges and a specified number of initial vertices and terminal vertices. In order to do s…
Graphlet and Orbit Computation on Heterogeneous Graphs
Colin Cleveland, Chin-Yen Lee, Shen-Fu Tsai +2
Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures…
Saturation of multidimensional 0-1 matrices
Shen-Fu Tsai
A 0-1 matrix is saturating for a 0-1 matrix if does not contain a submatrix that can be turned into by flipping any number of its -entries to -entries, and ch…
Peripherality in networks: theory and applications
Jesse Geneson, Shen-Fu Tsai
We investigate several related measures of peripherality and centrality for vertices and edges in networks, including the Mostar index which was recently introduced as a measure of…
Expected capture time and throttling number for cop versus gambler
Jesse Geneson, Carl Joshua Quines, Espen Slettnes +1
We bound expected capture time and throttling number for the cop versus gambler game on a connected graph with vertices, a variant of the cop versus robber game that is played…
Sharper bounds and structural results for minimally nonlinear 0-1 matrices
Jesse Geneson, Shen-Fu Tsai
The extremal function is the maximum possible number of ones in any 0-1 matrix with rows and columns that avoids . A 0-1 matrix is called minimally non-li…
Variations of the cop and robber game on graphs
Espen Slettnes, Carl Joshua Quines, Shen-Fu Tsai +1
We prove new theoretical results about several variations of the cop and robber game on graphs. First, we consider a variation of the cop and robber game which is more symmetric ca…
Computing optimal strategy for cop in the game of Cop v.s. Gambler
Shen-Fu Tsai
We present two efficient algorithms that compute the optimal strategy for cop in the game of Cop v.s. Gambler where the gambler's strategy is not optimal but known to the cop. The…
Two properties of maximal antichains in strict chain product posets
Shen-Fu Tsai
We present two results on maximal antichains in the strict chain product poset . First, we prove that these maximal antichains are al…