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Suppose that a graph class $\mathcal{C}$ is defined as follows:

A graph $G$ belongs to $\mathcal{C}$ if, and only if $G$ is chordal, but has at most $k$ $5$-cycles.

I am aware that the definition of $\mathcal{C}$ is contradictory. However, I am looking for a notation like

$G \in C_4\text{-free} + k*(C_5)$

Is there such notation in the literature?

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    $\begingroup$ Not a proper answer, but maybe a start: collections of graphs from classes and sets, so set notation is entirely applicable, for example: graphclasses.org/classes.cgi $\endgroup$ – Luke Mathieson Nov 28 '18 at 23:33
  • $\begingroup$ @LukeMathieson That is true, but the set notation has no limitations on the number of instances. $\endgroup$ – padawan Nov 29 '18 at 0:46

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