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A survey of degree-boundedness

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arxiv 2403.05737 v2 pith:C2GB66FE submitted 2024-03-09 math.CO

Xiying Du , Rose McCarty This is my paper · ORCID
classification math.CO
keywords degreedegree-boundednesslargeminimumsurveyareabalancedbicliques
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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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  1. Induced subgraphs of graphs with large deficiency

    math.CO 2025-05 conditional novelty 6.0 of 10

    Connected graphs with bounded local independence and only admitted odd or even bones have matching deficiency at most explicit extremal formulas.

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