Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers

Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers

Bibliographic Details
Main Author: Mutar, Mohammed A.
Language:English
Published: Wright State University / OhioLINK 2017
Subjects:
Mathematics
Signed graphs
Bidirection
Switching
Hamiltonicity
Ramsey numbers
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=wright1513377549200572
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-wright15133775492005722021-08-03T07:05:08Z Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers Mutar, Mohammed A. Mathematics Signed graphs Bidirection Switching Hamiltonicity Ramsey numbers Strong connectivity, 2-factors, and their relevance to Hamiltonicity, have been intensively studied on various classes of directed and 2-colored graphs. In chapter one, we define strong connectivity and bidirected 2-factors on bidirected graphs as a common genralization for both directed graphs and 2-colored graphs. We give necessary and sufficient conditions for the existence of bidirected Hamilton cycles in the following bidirected signed graphs: $\pm K_{n}$, $\pm K_{n,n}$, and $-K_{n,n}$. The Ramsey number problem is considered an interesting problem in graph theory which asks for the minimum positive integer $r$ that assures a 2-colored complete $K_r$ has a monochramatic clique $K_n$ or $K_m$. In chapter two, we define $r^*(n,m)$ to be the minimum positive integer that guarantees that any signing on $K_r$ has, up to switching, $-K_n$ or $+K_m$. Also, the following results are obtained: $r^*(n,m)=r^*(m,n)$, $r^*(n,m)\leq r(n-1,m-1)+1$, $ r^*(4,4)=7$, $r^*(4,5)=8$, and $10\leq r^*(4,6)\leq 15$. 2017 English text Wright State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=wright1513377549200572 http://rave.ohiolink.edu/etdc/view?acc_num=wright1513377549200572 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Mathematics
Signed graphs
Bidirection
Switching
Hamiltonicity
Ramsey numbers
spellingShingle Mathematics
Signed graphs
Bidirection
Switching
Hamiltonicity
Ramsey numbers
Mutar, Mohammed A.
Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers
author Mutar, Mohammed A.
author_facet Mutar, Mohammed A.
author_sort Mutar, Mohammed A.
title Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers
title_short Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers
title_full Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers
title_fullStr Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers
title_full_unstemmed Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed Numbers
title_sort hamiltonicity in bidirected signed graphs and ramsey signed numbers
publisher Wright State University / OhioLINK
publishDate 2017
url http://rave.ohiolink.edu/etdc/view?acc_num=wright1513377549200572
work_keys_str_mv AT mutarmohammeda hamiltonicityinbidirectedsignedgraphsandramseysignednumbers
_version_ 1719453361944657920

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