Connected graphs with bounded local independence and only admitted odd or even bones have matching deficiency at most explicit extremal formulas.
A survey of degree-boundedness
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abstract
Suppose a graph has no large balanced bicliques, but has large minimum degree. Then what can we say about its induced subgraphs? This question motivates the study of degree-boundedness, which is like $\chi$-boundedness but for minimum degree instead of chromatic number. We survey this area with an eye towards open problems.
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Induced subgraphs of graphs with large deficiency
Connected graphs with bounded local independence and only admitted odd or even bones have matching deficiency at most explicit extremal formulas.