如果一個圖形G 的頂點被分成k 個獨立子集，且彼此的頂點個數差最多為 一，則稱G 可均勻k -著色。一個圖形G 可均勻n 著色之最小整數n ，稱 為 G 的均勻著色數。任意n 大於k 且G 是均勻n 著色之最小整數k ，則 稱為G的均勻著色臨界數。在這篇論文中，我們主要探討的是：對一個二 部圖G，給定一常數k ，當其中一部分的點很少時，能對G 均勻著k 色(甚 至k以上)的條件，加以推廣後，也能刻劃一般的二部圖，能均勻著k 色( 甚至k以上)的條件． If the vertices of a graph G can be partitioned into k indepen- dent set and the difference of the sizes of any two sets is less than 1, then G is said to be equitably k-colorable. The smallest integer n for which G can be equitably n-colorable is called the equitable chromatic number of G. The smallest integer k for which G is equieably n-colorable for every n is greater than or equal to k is called the equitable threshold chromatic of G. In this thesis, we first discuss that: for a bipartite graph G, given a fixed number k, the sufficient condition to equitably k (even the number greater than k) -colorable on G, when one part of G has small size. Generalizing this result, we can classify the suffi- cient condition of G to be equitably k (even the number greater than k) -colorable.
