Abstract
A conjecture of Gallai states that if a graphG onn vertices contains no subgraph isomorphic to a wheel then the number of triangles inG is at mostn 2/8. In this note it is shown that this number is at most (1 +o(1))n 2/7, and in addition we exhibit a large family of graphs that shows that if the conjecture is true then there are many extremal examples.
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Haxell, P.E. A note on a conjecture of Gallai. Graphs and Combinatorics 11, 53–57 (1995). https://doi.org/10.1007/BF01787421
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DOI: https://doi.org/10.1007/BF01787421