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Symmetrically Continuous Functions, Marcin Szyszkowski
Symmetrically Continuous Functions, Marcin Szyszkowski
Graduate Theses, Dissertations, and Problem Reports
This work is devoted entirely to symmetric continuity and consists of five chapters. Chapter 1 is an introduction. Chapter 2, based on the paper [Sz2], is the main part of this work. In this chapter we generalize classic theorems on functions defined on the intervals to functions defined on arbitrary subsets of the real line. Chapter 3 deals with a weaker condition than symmetric continuity---weak symmetric continuity. It is an extended version of my paper [Sz1]. Chapter 4 is based on the paper [CSz]. Here it is shown that symmetrically continuous functions, although being "close" to continuous functions, may not …
Coloring Clique Hypergraphs, Hoifung Poon
Coloring Clique Hypergraphs, Hoifung Poon
Graduate Theses, Dissertations, and Problem Reports
Let G = (V, E) be a simple graph. The clique hypergraph of G, denoted as CH( G), has V as its set of vertices, and the maximal cliques as its hyperedges. Let Sk be a set of k colors. A map c : V Sk is a proper k-coloring for CH(G) if any maximal clique of G with at least two vertices receives at least two distinct colors. Let W ⊂ V, and let s ≥ 1. We say that G is (W, s)-extendible if any assignment on W with at most s colors can be extended to a …