叉连图的邻点可区别全染色

On Adjacent Vertex Distinguishing Total Colorings of Crossing Graphs

邻点可区别全染色猜想得到了国内外许多学者的关注和研究.迄今为止,这个猜想没有得到证明,也没有关于这个猜想的反例.叉连图对邻点可区别全染色猜想成立给予了证明,并给出了精确值.同时,证明了:存在无穷多个图,它们中的每一个图H至少包含一个真子图HH^1,使得x_as~″(H^1)>x_as~″(H).

Many researchers pay attention to the conjecture of adjacent-vertex distinguish- ing total chromatic number. This conjecture cannot solve and no counterexamples have been discovered up to now. We show that crossing graphs support the conjecture. Furthermore, we have proved that there are infinite graphs in which every graph H contains a proper subgraph H＇ such that Xas＂（H＇） 〉 Xas＂（H）.