Star extremal of circulant graphs

• Main Authors: Sheng-hsien Tu, 涂勝獻
• Other Authors: Xuding Zhu
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/55848476597136511381

碩士 === 國立中山大學 === 應用數學系研究所 === 92 === A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number. Given integers n,k,k'' such that 1<=k<=k''<=n/2,the circulant graph G(n,S_k,k'') has vertex set [n]={0,1,2,...,n-1} in which i~j if k<=|i-j|<=k'' or n-k''<= |i-j|<=n-k. It was known that for n=q(k+k'')+r,where 0<=r <k+k'', if k''>=5/4k,then G(n,S_k,k'') is star extremal. In the thesis, we prove that if k''>=7/6k and q>=4, then G(n,S_k,k'') is star extremal.