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Graph Theory and the Double-Critical...

Hanely, Derek W.

Graph Theory and the Double-Critical Conjecture.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Graph Theory and the Double-Critical Conjecture./
作者:	Hanely, Derek W.
面頁冊數:	1 online resource (62 pages)
附註:	Source: Masters Abstracts International, Volume: 56-06.
Contained By:	Masters Abstracts International56-06(E).
標題:	Mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9780355115369

Graph Theory and the Double-Critical Conjecture.
Hanely, Derek W.

Graph Theory and the Double-Critical Conjecture. - 1 online resource (62 pages)

Source: Masters Abstracts International, Volume: 56-06.

Thesis (M.S.)

Includes bibliographical references

A simple, connected graph is said to be double-critical if removing any pair of adjacent vertices lowers the chromatic number of the graph by exactly two. In 1966, Paul Erdo&huml;s and Laszlo Lovasz proposed the Double-Critical Conjecture which states that the complete graph is the only simple, connected graph that is a double-critical graph. This result has been proven when the chromatic number of a graph is less than six, but it has yet to be shown for the other cases. Ultimately, the purpose of this thesis is to further extend results related to this problem.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355115369Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Graph Theory and the Double-Critical Conjecture.
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100 1 $a Hanely, Derek W. $3 1180761
245 1 0 $a Graph Theory and the Double-Critical Conjecture.
264 0 $c 2017
300 $a 1 online resource (62 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Masters Abstracts International, Volume: 56-06.
500 $a Adviser: Rachelle R. Bouchat.
502 $a Thesis (M.S.) $c Indiana University of Pennsylvania $d 2017.
504 $a Includes bibliographical references
520 $a A simple, connected graph is said to be double-critical if removing any pair of adjacent vertices lowers the chromatic number of the graph by exactly two. In 1966, Paul Erdo&huml;s and Laszlo Lovasz proposed the Double-Critical Conjecture which states that the complete graph is the only simple, connected graph that is a double-critical graph. This result has been proven when the chromatic number of a graph is less than six, but it has yet to be shown for the other cases. Ultimately, the purpose of this thesis is to further extend results related to this problem.
520 $a In this thesis, the mathematical concepts related to this problem are discussed, and proofs of results related to the Double-Critical Conjecture are presented. Furthermore, this research introduces algorithms developed in the mathematics software package SageMath which can be used to analyze general graphs, test the double-critical condition on adjacent pairs of vertices, and extract particular induced subgraphs. Ideally, the work developed herein will fuel continued research on the Double-Critical Conjecture.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Indiana University of Pennsylvania. $b Mathematics. $3 1180762
773 0 $t Masters Abstracts International $g 56-06(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10283835 $z click for full text (PQDT)

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