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Class Ramsey numbers of cycles with chords versus books and fans

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  • Zhang, Yahui
  • Li, Yan
  • He, Changxiang

Abstract

Let Θn be the set of graphs formed by inserting an extra edge between any two non-adjacent vertices in Cn. Let E(Kr) → {red, blue} denote an edge-coloring where every edge of complete graph Kr is assigned red or blue. Defined the class Ramsey number R(F, Θn) to be the minimal positive integer r for which every E(Kr) → {red, blue} yields a monochromatic F in red or a monochromatic graph in family Θn in blue. We determine the precise value of R(Bm, Θn) for n≥8m9+112 with m ≥ 1000, and determine the asymptotical formulae of R(Bn(p),Θn) and R(Fn, Θ2⌊an⌋) as n → ∞. For a graph G with fewer than n vertices, let Cn(G) be a graph that consists of a Cn and additional edges forming a G. We shall generalize the mentioned results by replacing Θn with Cn(G).

Suggested Citation

  • Zhang, Yahui & Li, Yan & He, Changxiang, 2026. "Class Ramsey numbers of cycles with chords versus books and fans," Applied Mathematics and Computation, Elsevier, vol. 524(C).
    • Handle: RePEc:eee:apmaco:v:524:y:2026:i:c:s0096300326000986
    DOI: 10.1016/j.amc.2026.130046
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