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Chords Of Longest Circuits Of Graphs, Xuechao Li
Chords Of Longest Circuits Of Graphs, Xuechao Li
Graduate Theses, Dissertations, and Problem Reports
This thesis is on a long standing open conjecture proposed by one of the most prominent mathematicians, Dr. C. Thomassen: Every longest circuit of 3-connected graph has a chord. In 1987, C. Q. Zhang proved that every longest circuit of a 3-connected planar graph G has a chord if G is cubic or if the minimum degree is at least 4. In 1997, Carsten Thomassen proved that every longest circuit of 3-connected cubic graph has a chord.;In this dissertation, we prove the following three independent partial results: (1) Every longest circuit of a 3-connected graph embedded in a projective plane …
Dynamic Coloring Of Graphs, Bruce Montgomery
Dynamic Coloring Of Graphs, Bruce Montgomery
Graduate Theses, Dissertations, and Problem Reports
In this dissertation, we introduce and study the idea of a dynamic coloring of a graph, a coloring in which any multiple-degree vertex of the graph must be adjacent to at least two color classes.;As parts of the overall research, 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 coloring.;The interesting subjects of colorings we consider are the chromatic number of important graphs, upper bounds of the …
Set-Theoretic And Algebraic Properties Of Certain Families Of Real Functions, Krzysztof Plotka
Set-Theoretic And Algebraic Properties Of Certain Families Of Real Functions, Krzysztof Plotka
Graduate Theses, Dissertations, and Problem Reports
Given two families of real functions F1 and F2 we consider the following question: can every real function f be represented as f = f 1 + f2, where f1 and f2 belong to F1 and F2 , respectively? This question leads to the definition of the cardinal function Add: Add( F1,F2 ) is the smallest cardinality of a family F of functions for which there is no function g in F1 such that g + F is contained in F2 . This work is devoted entirely to the study of the function Add for different pairs of families of …