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{\bf Stephan Brandt and Toma\v{z} Pisanski}
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{\bf Another Infinite Sequence of Dense Triangle-Free Graphs}
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The {\it core} is the unique homorphically minimal subgraph of a graph.
A triangle-free graph with minimum degree $\delta > n/3$ is called {\it dense.}
It was observed by many authors that dense triangle-free graphs share strong
structural properties and that the
natural way to describe the structure of these graphs is in terms of
graph homomorphisms. One infinite sequence of
cores of dense maximal triangle-free graphs was known.
All graphs in this sequence are 3-colourable. Only
two additional cores with chromatic number 4 were known. We show that
the additional graphs are the initial terms of a second infinite sequence of cores.
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