关于临界图的一个定理的推广(英文)

An Extension of One Theorem of Critical Edge chromatic Graphs

叶宏博证明了当Δ≥５时没有度序列是２ｒΔ２ｒ的Δ－临界图．Ｋａｙａｔｈｒｉ推广了上述结果，证明了当Δ≥５时，没有同时满足下列两个条件的Δ－临界图：（ａ）Ｇ有一个２度点ｘ；设ｙ，ｚ是ｘ的两个邻接点；（ｂ）有一主项点ｙ１∈ＮＧ（ｙ）（ｙ１≠ｙ）与－２度点邻接．我们对上述结果进一步推广，证明了条件（ｂ）不是必要的；只要ｙ１与一个度数小于Δ－１的点邻接即可（可以不是２度点）．

Yap proved that there is no Δ critical graph (Δ≥5) with degree list 2 rΔ 2r . Kayathri generalized it by showing that there is no Δ critical graph G(Δ≥5) with the following properties :(a) G has a vertex x of degree 2;let y,z be the neighbours of x ;(b) There is a (major) vertex y 1∈N G(y)(y 1≠x) which is adjacent to a vertex of degree 2.We again generalized the above by showing that the assumption (b) is unnecessary;it is enough that y 1 is adjacent to a vertex of degree less than Δ 1(maybe not of degree 2).