Abstract
We determine the maximum number of edges that a chordal graph G can have if its degree, \(\varDelta (G)\), and its matching number, \(\nu (G)\), are bounded. To do so, we show that for every \(d,\nu \in \mathbb {N}\), there exists a chordal graph G with \(\varDelta (G)<d\) and \(\nu (G)<\nu \) whose number of edges matches the upper bound, while having a simple structure: G is a disjoint union of cliques and stars.
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Blair, J.R.S., Heggernes, P., Lima, P.T. et al. On the Maximum Number of Edges in Chordal Graphs of Bounded Degree and Matching Number. Algorithmica 84, 3587–3602 (2022). https://doi.org/10.1007/s00453-022-00953-9
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DOI: https://doi.org/10.1007/s00453-022-00953-9