Abstract
An orientation of a complete graph is a tournament, and an orientation of a complete c -partite graph is a c -partite tournament. If x is a vertex of a digraph D , then we denote by d + ( x ) and d - ( x ) the outdegree and the indegree of x , respectively. The global irregularity of a digraph D is defined by i g ( D ) = max { d + ( x ) , d - ( x ) } - min { d + ( y ) , d - ( y ) } over all vertices x and y of D (including x = y ). If i g ( D ) = 0 , then D is regular and if i g ( D ) ⩽ 1 , then D is called almost regular. In 1999, L. Volkmann showed that, if D is an almost regular c -partite tournament with c ⩾ 4 , then D contains a strongly connected subtournament of order p for every p ∈ { 3 , 4 , … , c - 1 } and he conjectured that this also holds for p = c , if c ⩾ 5 . In this paper, we settle this conjecture in affirmative.
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