A unified framework yields eight depth measures on matroids with six shown functionally inequivalent, two matching branch-depth and tree-depth, and all coinciding on matroids versus matrices over any field.
Branch-depth: Generalizing tree-depth of graphs
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The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.
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Measuring Depth of Matroids
A unified framework yields eight depth measures on matroids with six shown functionally inequivalent, two matching branch-depth and tree-depth, and all coinciding on matroids versus matrices over any field.
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An Overview of Universal Obstructions for Graph Parameters
The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.