Opuscula Math. 37, no. 4 (2017), 589-595

Opuscula Mathematica

Toward Wojda's conjecture on digraph packing

Jerzy Konarski
Andrzej Żak

Abstract. Given a positive integer \(m\leq n/2\), Wojda conjectured in 1985 that if \(D_1\) and \(D_2\) are digraphs of order \(n\) such that \(|A(D_1)|\leq n-m\) and \(|A(D_2)|\leq 2n-\lfloor n/m\rfloor-1\) then \(D_1\) and \(D_2\) pack. The cases when \(m=1\) or \(m = n/2\) follow from known results. Here we prove the conjecture for \(m\geq\sqrt{8n}+418275\).

Keywords: packing, digraph, size.

Mathematics Subject Classification: 05C35.

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Cite this article as:
Jerzy Konarski, Andrzej Żak, Toward Wojda's conjecture on digraph packing, Opuscula Math. 37, no. 4 (2017), 589-595, http://dx.doi.org/10.7494/OpMath.2017.37.4.589

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