Abstract
The strong chromatic index s ′ ( G ) is the minimum integer t such that there is an edge-coloring of G with t colors in which every color class is an induced matching. Brualdi and Quinn conjecture that for every bipartite graph G, s ′ ( G ) is bounded by Δ 1 Δ 2 , where Δ 1 and Δ 2 are the maximum degrees among vertices in the two partite sets. We give the affirmative answer for Δ 1 = 2 .
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