Gyárfás, A. The irregularity strength of \(K_{m,m}\) is 4 for odd m. (English) Zbl 0681.05066 Discrete Math. 71, No. 3, 273-274 (1988). G. Chartrand et al. showed that for odd m, \(m\geq 3\), the edges of \(K_{m,m}\) can be labelled with 1, 2, 3, 4 in such a way that the (weighted) degrees of the vertices are all different. They conjectured that no such labelling exists with labels 1, 2, 3. In this note we prove this conjecture. G. Chartrand et al. showed that for odd m, \(m\geq 3\), the edges of \(K_{m,m}\) can be labelled with 1, 2, 3, 4 in such a way that the (weighted) degrees of the vertices are all different. They conjectured that no such labelling exists with labels 1, 2, 3. In this note we prove this conjecture. Reviewer: R.C.Read Cited in 16 Documents MSC: 05C99 Graph theory Keywords:edge-labelling PDFBibTeX XMLCite \textit{A. Gyárfás}, Discrete Math. 71, No. 3, 273--274 (1988; Zbl 0681.05066) Full Text: DOI References: [1] G. Chartrand, M. Jacobson, J. Lebel, O. Oellerman, S. Ruiz and F. Saba, Irregular networks, Submitted to Fort Wayne Conference Proceedings.; G. Chartrand, M. Jacobson, J. Lebel, O. Oellerman, S. Ruiz and F. Saba, Irregular networks, Submitted to Fort Wayne Conference Proceedings. [2] R. Faudree, M. Jacobson, J. Lehel and R. H. Schelp, Irregular networks, Regular graphs and integer matrices with distinct row and column sums, Submitted to Discrete Math.; R. Faudree, M. Jacobson, J. Lehel and R. H. Schelp, Irregular networks, Regular graphs and integer matrices with distinct row and column sums, Submitted to Discrete Math. · Zbl 0685.05029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.