Solutions and Problems

Patrick added the Max-even-minus-even-horizontal lower bound to his code. (It was previously in my code – but now we’ve moved exclusively to his). This solved the graph GCR~vo.

The next run of the program produced the graph GCrb‘o, pictured below.

This graph was only difficult momentarily. Patrick recognized that it was triangle-free and that one of the “special bounds” mentioned in the survey on bounds applies, namely Fajtlowicz’s bound 5n/14 lower bound for triangle-free graphs with maximum degree no more than 3. So its solved now too. Here’s the newest difficult graph:


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