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Regular Turán numbers and some Gan–Loh–Sudakov‐type problems
Author(s) -
Cambie Stijn,
Joannis de Verclos Rémi,
Kang Ross J.
Publication year - 2023
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22857
Subject(s) - mathematics , combinatorics , class (philosophy) , type (biology) , graph , natural number , discrete mathematics , computer science , ecology , artificial intelligence , biology
Motivated by a Gan–Loh–Sudakov‐type problem, we introduce the regular Turán numbers, a natural variation on the classical Turán numbers where we restrict ourselves to the class of regular graphs. Among other results, we prove a striking supersaturation version of Mantel's theorem in the case of a regular host graph of odd order. We also characterize the graphs for which the regular Turán numbers behave classically or otherwise.