Some notes on the signed bad number in bipartite graphs

DOI10.1142/S1793830920920019arXiv1809.08460MaRDI QIDQ6307102

Publication date: 22 September 2018

Abstract: In this paper, we deal with the signed bad number and the negative decision number of graphs. We show that two upper bounds concerning these two parameters for bipartite graphs in papers [Discrete Math. Algorithms Appl. 1 (2011), 33--41] and [Australas. J. Combin. 41 (2008), 263--272] are not true as they stand. We correct them by presenting more general bounds for triangle-free graphs by using the classic theorem of Mantel from the extremal graph theory and characterize all triangle-free graphs attaining these bounds.

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graph labelling (graceful graphs, bandwidth, etc.) (05C78) Conference proceedings and collections of articles (00Bxx)

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