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Showing 1 to 20 of 41 for “"Colorings"”.
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Colorings and list colorings of graphs and hypergraphs
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-04-04T13:50:38Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 thesis.tex: 208138 bytes, checksum: 3f2bbfe42b155982f3fe9f0f51b4e863 (MD5) config1.eps: 12369 bytes, checksum: …
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Graphs, codes, and colorings
Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2010-11-24T20:52:49Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Kantor_Ida.pdf: 588064 bytes, checksum: ed396002d8eb12e47e04cf8040eb7e99 (MD5)
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Colorings of sparse graphs and multigraphs
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms
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Extremal problems on special graph colorings
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms
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Extremal problems on variations of graph colorings
This thesis investigates various coloring problems in graph theory. Graph coloring is an essential part of combinatorics and discrete mathematics, as it deals with the fundamental problem of partitioning objects so that each part satisfies a certain condition. In particular, we study how forbidding …
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An Introduction to List Colorings of Graphs
… and useful areas of graph theory is graph colorings. A graph coloring is an assignment of integers to the vertices of a graph so that no two adjacent vertices are assigned the same integer. This problem frequently arises in scheduling and channel assignment applications. A list coloring of …
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Coincidences and colorings of lattices and Z-modules
… problem for sublattices and submodules, colorings of lattices and Z-modules, shifted lattices and shifted Z-modules, and multilattices. Moreover, the idea of a coincidence isometry of a lattice or Z-module is extended to include general (affine) isometries. The first chapter gives all the …
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Edge-colorings and flows in Class 2 graphs
We consider edge-colorings and flows problems in Graph Theory that are hard to solve for Class 2 graphs. Most of them are strongly related to some outstanding open conjectures, such as the Cycle Double Cover Conjecture, the Berge-Fulkerson Conjecture, the Petersen Coloring Conjecture and the …
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Games on graphs, visibility representations, and graph colorings
"In this thesis we study combinatorial games on graphs and some graph parameters whose consideration was inspired by an interest in the symmetry of hypercubes. A capacity function f on a graph G assigns a nonnegative integer to each vertex of V(G). An f-matching in G is a set M ⊆ E(G) such that the …
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Combinatorial Problems on the Integers: Colorings, Games, and Permutations
<p>This dissertation consists of several combinatorial problems on the integers. These problems fit inside the areas of extremal combinatorics and enumerative combinatorics.</p> <p>We first study monochromatic solutions to equations when integers are colored with finitely many colors in Chapter 2. …
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Extremal problems on cycle structure and colorings of graphs
This Dissertation was approved for publication on 2016-07-07 at 14:43.
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Extremal Problems in Graph Theory: Degree Sequences, Distance, Colorings, and Labelings
Let f(n, p, q) be the minimum number of colors required to color the edges of Kn in such a way that the edges of every Kp⊆Kn together receive at least q colors. We focus on determining f(n, 4, 3) and prove a constructive upper bound of eOlogn . This improves on the previous best …
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Extremal problems on edge-colorings, independent sets, and cycle spectra of graphs
… in extremal graph theory with respect to edge-colorings, independent sets, and cycle spectra. In Chapters 2 and 3, we present results in Ramsey theory, where we seek Ramsey host graphs with small maximum degree. In Chapter 4, we study a Ramsey-type problem on edge-labeled trees, where we seek …
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Competitive versions of vertex ranking and game acquisition, and a problem on proper colorings
… graph G^j_k(H), whose vertices are the proper k-colorings of a given graph H, with edges joining colorings that differ only on a set of vertices contained within a connected subgraph of H on at most j vertices. We introduce and study the parameters g_k(H) and h_k(H), which denote the minimum j …
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Dynamic coloring of graphs
… we study (for some interesting subjects of colorings) the corresponding subjects of dynamic colorings, we compare the chromatic number and dynamic chromatic number, and we study some problems unique to dynamic colorings. Also, we introduce and briefly study a generalization of dynamic …
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Enumerating combinatorial objects with limited sub-configurations
… we investigate an enumeration problem on Gallai colorings, i.e. rainbow triangle-free colorings. In particular, we describe the typical structure of Gallai r-colorings of complete graphs, and complete the characterization of the extremal graphs for Gallai colorings. This work heavily relies on …
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Boethian Colorings in Geoffrey Chaucer's Earlier Poetry: The Book of the Duchess, The Parliament of Fowls and The House of Fame
There has been much written on Boethius and his impact on Chaucer's greater known works, such as The Canterbury Tales and Troilus and Criseyde, yet there has not been much light shone on his other works, namely The Book of the Duchess, The Parliament of Fowls, and The House of Fame, which are a …
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Coloring Problems on Graphs and Hypergraphs
… by Erdo&huml;s and Gyarfas. We interpret such colorings using a two-round game against an adversary; this relates splittable colorings to classical Ramsey numbers. Let fr(m) be the least n such that some r-edge-coloring of K n is not (r, m)-splittable. Combinatorial designs yield fr(m) ≤ …
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Pólya's Enumeration Theorem and Its Applications
… of PET, it is applied to the enumerations of colorings of polytopes of dimension 2 and 3, including necklaces, the cube, and the truncated icosahedron. The general formulas for the number of n-colorings of the latter two are also derived. In number theory, work by Chong-Yun Chao is presented, …
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The Chromatic MacMahon Function
We examine colorings of weighted graphs. Firstly, we examine the weighted analogue of Stanley’s chromatic symmetric function, and prove that the weighted analogue of Crew’s conjecture is not true. Secondly, we generalize the chromatic symmetric function to the chromatic MacMahon function, and use …
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