The t-Tone Coloring of Kneser Graphs KG(n,2)

• Main Authors: TSAI, CHENG-HSIU, 蔡政修
• Other Authors: PAN, JUN-JIE
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/52881537415226571252

碩士 === 輔仁大學 === 數學系碩士班 === 103 === A t-tone k-coloring of a graph G is a function f:V(G)→{[k] choose t} such that |f(u) ∩ f(v)| < d(u,v) for all distinct vertices u and v. The t-tone chromatic number of G, denoted τ_{t}(G), is the smallest positive integer k such that G has a t-tone k-coloring. For n ≥ 2k, the Kneser graph KG(n,k) is the graph whose vertex set is the collection of all k-subsets of [n], and two vertices are adjacent if and only if they are disjoint. In this thesis, we give a lower bound of the t-tone chromatic number of a graph and use a linear programming approach to obtain a lower bound of the t-tone chromatic number of KG(n,2). Moreover, we determine the t-tone chromatic number of KG(5,2).