Cater, Steven C.; Harary, Frank; Robinson, Robert W. One-color triangle avoidance games. (English) Zbl 0990.91008 Congr. Numerantium 153, 211-221 (2001). In the triangle avoidance game two players take turns to add edges to a graph which initially consists of \(n\) nodes and no edges. The first player to complete a triangle (3-cycle) loses. This paper describes a computation to determine which player has a winning strategy when \(n\leq 12\). The winner for \(n\leq 9\) had previously been determined by Á. Seress [Graphs Comb. 8, No. 1, 75-79 (1992; Zbl 0757.90096)]. The authors also solve the simple game in which the aim is to avoid creating any cycle of odd-length, showing that the first player to move wins when \(n\) is 2 modulo 4 and otherwise the second player wins. Reviewer: Ian M.Wanless (Oxford) Cited in 4 Documents MSC: 91A43 Games involving graphs 05C20 Directed graphs (digraphs), tournaments Keywords:graph games; avoidance games; triangle-free graph Citations:Zbl 0757.90096 PDFBibTeX XMLCite \textit{S. C. Cater} et al., Congr. Numerantium 153, 211--221 (2001; Zbl 0990.91008)