Abstract
A bull is a graph with five vertices a, b, c, d, e and five edges ab, bc, cd, be, ce. A graph G is bull-reducible if no vertex of G lies in two bulls. An even pair is a pair of vertices such that every chordless path joining them has even length. We prove that for every bull-reducible Berge graph G with at least two vertices, either G or its complementary graph \( \bar G \) has an even pair.
This research was partially supported by CNPq, CAPES (Brazil)/COFECUB (France), project number 359/01.
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de Figueiredo, C.M.H., Maffray, F., Maciel, C.R.V. (2006). Even Pairs in Bull-reducible Graphs. In: Bondy, A., Fonlupt, J., Fouquet, JL., Fournier, JC., Ramírez Alfonsín, J.L. (eds) Graph Theory in Paris. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7400-6_14
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