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For a connected graph G of order n and minimum degree δ we prove the existence of two disjoint dominating sets D1 and D2 such that, if δ ≥ 2, then |D1∪D2| ≤ 67n unless G = C4, and, if δ ≥ 5, then |D1 ∪ D2| ≤ 2 δ+1 n. While for the first estimate there are exactly six extremal graphs which are all of order 7, the second estimate is asymptotically best-possible.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1978-0464595-0