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Full-Text Articles in Discrete Mathematics and Combinatorics
3-Uniform 4-Path Decompositions Of Complete 3-Uniform Hypergraphs, Rachel Mccann
3-Uniform 4-Path Decompositions Of Complete 3-Uniform Hypergraphs, Rachel Mccann
Mathematical Sciences Undergraduate Honors Theses
The complete 3-uniform hypergraph of order v is denoted as Kv and consists of vertex set V with size v and edge set E, containing all 3-element subsets of V. We consider a 3-uniform hypergraph P7, a path with vertex set {v1, v2, v3, v4, v5, v6, v7} and edge set {{v1, v2, v3}, {v2, v3, v4}, {v4, v5, v6}, {v5, v6 …
Minimality Of Integer Bar Visibility Graphs, Emily Dehoff
Minimality Of Integer Bar Visibility Graphs, Emily Dehoff
University Honors Theses
A visibility representation is an association between the set of vertices in a graph and a set of objects in the plane such that two objects have an unobstructed, positive-width line of sight between them if and only if their two associated vertices are adjacent. In this paper, we focus on integer bar visibility graphs (IBVGs), which use horizontal line segments with integer endpoints to represent the vertices of a given graph. We present results on the exact widths of IBVGs of paths, cycles, and stars, and lower bounds on trees and general graphs. In our main results, we find …
Matrix Interpretations And Tools For Investigating Even Functionals, Benjamin Stringer
Matrix Interpretations And Tools For Investigating Even Functionals, Benjamin Stringer
Theses and Dissertations--Computer Science
Even functionals are a set of polynomials evaluated on the terms of hollow symmetric matrices. Their properties lend themselves to applications such as counting subgraph embeddings in generic (weighted or unweighted) host graphs and computing moments of binary quadratic forms, which occur in combinatorial optimization. This research focuses primarily on counting subgraph embeddings, which is traditionally accomplished with brute-force algorithms or algorithms curated for special types of graphs. Even functionals provide a method for counting subgraphs algebraically in time proportional to matrix multiplication and is not restricted to particular graph types. Counting subgraph embeddings can be accomplished by evaluating a …