DECOMPOSITION OF COMPLETE GRAPHS INTO TRIANGLES AND CLAWS

LetKn be a complete graph withnvertices,Ck denote a cycle of lengthk, andSk denote a star withkedges. Ifk= 3, then we callC 3a triangle andS3 a claw. In this paper, we show that for any nonnegative integerspandqand any positive integern, there exists a decomposition ofKn intopcopies ofC3 andqcopies...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 18; no. 5; pp. 1563 - 1581
Main Authors Fu, Chin-Mei, Lin, Yuan-Lung, Lo, Shu-Wen, Hsu, Yu-Fong
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.10.2014
Subjects
Claws
Integers
Mathematical sets
Necessary conditions
Vertices
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ISSN1027-5487
2224-6851
2224-6851
DOI10.11650/tjm.18.2014.3169

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Summary:LetKn be a complete graph withnvertices,Ck denote a cycle of lengthk, andSk denote a star withkedges. Ifk= 3, then we callC 3a triangle andS3 a claw. In this paper, we show that for any nonnegative integerspandqand any positive integern, there exists a decomposition ofKn intopcopies ofC3 andqcopies ofS3 if and only if 3 ( p + q ) = ( n 2 ) ,q≠1, 2 ifnis odd,q=1 ifn= 4, and q ≥ max { 3 , ⌈ n 4 ⌉ } ifnis even andn≥ 6. 2010Mathematics Subject Classification: 05C51. Key words and phrases: Graph decomposition, Complete graph, Cycle, Star.
ISSN:1027-5487
2224-6851
2224-6851
DOI:10.11650/tjm.18.2014.3169