K3,5,p的点可区别的一般全染色

首先, 利用色集合事先分配法, 反证探讨完全三部图K_3,5,p(p≥5)的点可区别一般全色数, 给出当p较小时的特殊性证明以及当p逐渐增大时的规律性证明； 其次, 利用构造染色法对完全三部图K_3,5,p进行染色, 给出染色方案. 染色的成功验证了反证法所证明色数的正确性, 从而解决了完全三部图K_3,5,p的点可区别一般全染色问题.

Vertex-Distinguishing General Total Coloring of K3,5,p

Firstly, we discussed vertex-distinguishing general total chromatic number of complete tripartite graphs K_3,5,p(p≥5) by using the method of distributing the color sets in advance and contradiction, and gave special proofs when p was small and regular proofs when p increased gradually. Secondly, we used the methods of constructing the colorings to dye the complete tripartite graphs K_3,5,p, and gave a  coloring scheme. The success of the coloring verified the correctness of the color number proved by the contradiction method, thus we solved the problem of vertex-distinguishing general total coloring of complete tripartite graphs K_3,5,p.