József Balogh, Anita Liebenau, Letícia Mattos, Natasha Morrison
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SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2297-2311, September 2024. Abstract. We address a problem which is a generalization of Turán-type problems recently introduced by Imolay, Karl, Nagy, and Váli. Let [math] be a fixed graph and let [math] be the union of [math] edge-disjoint copies of [math], namely [math], where each [math] is isomorphic to a fixed graph [math] and [math] for all [math]. We call a subgraph [math] multicolored if [math] and [math] share at most one edge for all [math]. Define [math] to be the maximum value [math] such that there exists [math] on [math] vertices without a multicolored copy of [math]. We show that [math] and that all extremal graphs are close to a blow-up of the 5-cycle. This bound is tight up to the linear error term.
期刊介绍：
SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution.
Topics include but are not limited to:
properties of and extremal problems for discrete structures
combinatorial optimization, including approximation algorithms
algebraic and enumerative combinatorics
coding and information theory
additive, analytic combinatorics and number theory
combinatorial matrix theory and spectral graph theory
design and analysis of algorithms for discrete structures
discrete problems in computational complexity
discrete and computational geometry
discrete methods in computational biology, and bioinformatics
probabilistic methods and randomized algorithms.
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