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The k -restricted arc connectivity of digraphs is a common generalization of the arc connectivity and the restricted arc connectivity. An arc subset S of a strong digraph D is a k -restricted arc cut if D − S has a strong component D ′ with order at least k such that D − V ( D ′ ) contains a connected subdigraph with order at least k . The k -restricted arc connectivity...
For a graph G , the supereulerian width μ ′ ( G ) of a graph G is the largest integer s such that G has a spanning ( k ; u , v ) -trail-system, for any integer k with 1 ≤ k ≤ s , and for any u , v ∈ V ( G ) with u ≠ v . Thus μ ′ ( G ) ≥ 2 implies that G is supereulerian, and so graphs with higher supereulerian width are natural generalizations of supereulerian...
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