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Full-Text Articles in Physical Sciences and Mathematics
Elements Of Convergence Approach Theory, William D. Trott
Elements Of Convergence Approach Theory, William D. Trott
Electronic Theses and Dissertations
We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.
Precise Partitions Of Large Graphs, Pouria Salehi Nowbandegani
Precise Partitions Of Large Graphs, Pouria Salehi Nowbandegani
Electronic Theses and Dissertations
First by using an easy application of the Regularity Lemma, we extend some known results about cycles of many lengths to include a specified edge on the cycles. The results in this chapter will help us in rest of this thesis. In 2000, Enomoto and Ota posed a conjecture on the existence of path decomposition of graphs with fixed start vertices and fixed lengths. We prove this conjecture when |G| is large. Our proof uses the Regularity Lemma along with several extremal lemmas, concluding with an absorbing argument to retrieve misbehaving vertices. Furthermore, sharp minimum degree and degree sum conditions …