关于二部图K(m,n)-A(|A|= 2)的色唯一性的一个注记(英文)

Note on the Chromaticity of the Bipartite Graph K(m,n) -A with |A| = 2

设Ｋ（ｍ，ｎ）－Ａ表示从完全二部图Ｋ（ｍ，ｎ）中删去子边集Ａ所得之图，Ｋ（ｍ，ｎ）［Ａ］表示由Ａ导出的 Ｋ（ｍ，ｎ）的子图，（Ｍ，Ｎ）表示 Ｋ（ｍ，ｎ）的一部分，其中｜Ｍ｜＝ ｍ， ｜Ｎ｜＝ ｎ．文章证明了：当 ｍ ≥ ３，｜Ａ｜＝２时，Ｋ（ｍ，ｍ）－Ａ（其中Ｋ（３，３）［Ａ］≠Ｋ（１，２）），Ｋ（ｍ，ｍ＋１）－Ａ和Ｋ（ｍ，ｍ＋２）－Ａ（其中Ｋ（３，５）［Ａ］ Ｋ（１，２）和｜Ｖ（Ｋ（３，５）［Ａ］）∩Ｍ｜＝２不同时成立）均是色唯一图．

Let K(m, n ) - A denote the bipartite graph obtained by deleting a set of edges A froma complete bipartite graph K(m , n ) ,K(m ,n ) [A] denote the subgraph of K(m, n ) inducedby A and (M,N) denote the bipartition of V(K(m, n)),Where |M| = m and |N | = n, In this pape we prove that if m ≥ 3 and |A| = 2,K(m,n) - A (where K(3,3)[A] K(1,2)), K(m, m +1) - A and K(m,m + 2) - A (Where it does not hold that K(3,5)[A] K(1,2) and | V(K(3,5) [A] ) ∩ M | = 2) are all chromatically unique.