As with our original example, this result about triangle-free graphs is related to the Erdős-Hajnal conjecture. If a graph is triangle-free, then it can’t have a clique larger than size 2, since a ...

Meanwhile, seminal work on triangle‐free intersection graphs of line segments has demonstrated that even in the absence of triangular substructures the chromatic number can be unbounded [2].

Abstract. In this paper, we study the problem of determining the largest number of maximum independent sets of a graph of order n. Solutions to this problem are given for various classes of graphs, ...