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<p>We establish the <i>e</i>-positivity of cycle-chord graphs using the composition method which is developed by Zhou and the author recently. Our method is simpler than the (<i>e</i>)-positivity approach which is used for handling cycle-chords with girth at most 4. We also provide a combinatorial interpretation of the <i>e</i>-coefficients, and conjecture the <i>e</i>-positivity of theta graphs.</p>

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All Cycle-Chords are e-Positive

  • 期刊论文

  • 发表日期：

    2025年3月26日

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  • David G. L. Wang

摘要

We establish the e-positivity of cycle-chord graphs using the composition method which is developed by Zhou and the author recently. Our method is simpler than the (e)-positivity approach which is used for handling cycle-chords with girth at most 4. We also provide a combinatorial interpretation of the e-coefficients, and conjecture the e-positivity of theta graphs.