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Planar Graphs, Biplanar Graphs And Graph Thickness, Sean M. Hearon
Planar Graphs, Biplanar Graphs And Graph Thickness, Sean M. Hearon
Electronic Theses, Projects, and Dissertations
A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this thesis, we determine the smallest complete and complete bipartite graphs that are not biplanar.
Abstractions And Analyses Of Grid Games, Taylor Rowan Boone
Abstractions And Analyses Of Grid Games, Taylor Rowan Boone
Senior Projects Spring 2016
In this paper, we define various combinatorial games derived from the NQueens Puzzle and scrutinize them, particularly the Knights Game, using combinatorial game theory and graph theory. The major result of the paper is an original method for determining who wins the Knights Game merely from the board's dimensions. We also inspect the Knights Game's structural similarities to the Knight's Tour and the Bishops Game, and provide some historical background and real-world applications of the material.
Fibonomial Tilings And Other Up-Down Tilings, Robert Bennett
Fibonomial Tilings And Other Up-Down Tilings, Robert Bennett
HMC Senior Theses
The Fibonomial coefficients are a generalization of the binomial coefficients with a rather nice combinatorial interpretation. While the ordinary binomial coefficients count lattice paths in a grid, the Fibonomial coefficients count the number of ways to draw a lattice path in a grid and then Fibonacci-tile the regions above and below the path in a particular way. We may forgo a literal tiling interpretation and, instead of the Fibonacci numbers, use an arbitrary function to count the number of ways to "tile" the regions of the grid delineated by the lattice path. When the function is a combinatorial sequence such …