Sharp Spectral Inequalities for Graphs via Majorization and Schur-Convexity [r-libre/4186]

Bouthat, Ludovick, Mashreghi, Javad et Morneau-Guérin, Frédéric ORCID: https://orcid.org/0000-0001-7610-4648 (07 aout 2026). Sharp Spectral Inequalities for Graphs via Majorization and Schur-Convexity. Communication (sur invitation) présentée à la International Workshop on Operator Theory and its Applications (IWOTA) 2026, Québec.

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Catégorie de document :	Communications à des congrès/colloques et conférences (non publiées)
Évaluation par un comité de lecture :	Non
Étape de publication :	Non publié
Résumé :	We present an approach to derive sharp spectral inequalities for simple graphs based on majorization theory and Schur-convexity. By comparing the spectrum of an arbitrary graph with those of extremal models such as complete, complete bipartite, and matching graphs, we obtain a systematic way to generate inequalities involving the extreme eigenvalues lambda_1, $\|lambda_n\|$, and spectral norms. The key idea is that every positive Schur-convex spectral functional produces a family of sharp inequalities, so proving graph inequalities reduces to choosing a suitable functional. We study this choice using random vector norms, where moment and cumulant expansions connect the framework to counts of closed walks in graphs. This perspective not only recovers several classical spectral inequalities in a unified framework, but also yields new sharp bounds, particularly in structured settings such as triangle-free and square-free graphs.
Adresse de la version officielle :	https://iwota-2026.fsg.ulaval.ca/
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	11 aout 2026 18:33
Dernière modification :	14 aout 2026 14:15

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