Degree sequence conditions for maximally edge-connected graphs depending on the clique number

Theorem 1 was the starting point for many other suÆ ient onditions for = Æ. Lesniak [9℄ weakened the ondition Æ bn=2 to deg(u) + deg(v) n for all pairs of nonadja ent verti es u and v in G. Plesn k [10℄ showed that every graph of diameter 2 satis es = Æ and thus generalized Lesniak's result. Improvements of Plesn k's result an be found in Plesn k, Zn am [11℄ and Dankelmann, Volkmann [4℄ (see also the textbook of Volkmann [11, p. 318 ℄). Goldsmith and White [8℄ proved that it is suÆ ient to have bn=2 disjoint pairs of verti es u i ; v i with deg(u i )+deg(v i ) n. Bollob as [1℄ gave a degree sequen e ondition that in ludes the ondition of Goldsmith and White for odd n. Xu [16℄ gave an analogue for dire ted graphs to the result by Goldsmith and White. Dankelmann and Volkmann [5℄ generalized Bollob as' and Xu's results and gave analogous degree onditions for bipartite graphs. Further onditions for = Æ, depending on parameters not dire tly related to the vertex degrees, (e.g. girth and diameter) are given in [6℄. If the graph ontains no omplete subgraph of order p+1, denoted by K p+1 , the above onditions an be weakened. Dankelmann and Volkmann [4℄ gave the following result, whi h was rst proved by Volkmann [13, 14℄ for p-partite graphs.