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math.RT2026

Derived Picard reconstruction for graded surfaces with stops

Wen Chang, Dongjian Wu

We study reconstruction of graded surfaces with stops from their mapping class groups and the derived Picard groups of their partially wrapped Fukaya categories. In genus…

math.CO2026

Degree-square Turán problem for two self-converse tournaments

Zhuoran Han, Yaojun Chen

For a fixed digraph , let be the maximum of over all -vertex -free digraphs. Ai et al. [arXiv:2606.03520, 2026] a…

math.CO2026

Ramsey multiplicity and extremal colorings for odd cycles

Ting Huang, Junying Lu, Jiabao Yang +1

The Ramsey number of a graph is the minimum positive integer such that every red/blue edge-coloring of the complete graph on vertices contains a monochroma…

math.CO2026

Counterexamples to two conjectures on the diameter of clique-free graphs

Hangdi Chen, Yaojun Chen

Erdős et al. (JCT-B, 1989) conjectured that, for integers and with , every connected -free graph of order and minimum degree has diam…

math.CO2026

New upper bound for the Ramsey number of odd cycles

Ting Huang, Jiabao Yang, Yaojun Chen

The \emph{-color Ramsey number} is the least integer such that any -edge-coloring of a complete graph has a monochromatic odd cycle …

math.CO2026

Erdős--Ko--Rado theorems in -norm for three finite spaces

Qian Bao, Yaojun Chen, Yanbo Zhang

Let be a -uniform hypergraph. The famous Erdős--Ko--Rado (1961) theorem determines the maximum size and extremal structure for being -intersecting…

math.CO2026

On monochromatic path covers conjecture of Erdős--Gyárfás

Hangdi Chen, Yaojun Chen

Erdős and Gyárfás conjectured in 1995 that, in every red--blue edge-coloring of a complete graph , the vertex set can be covered by at most monochromatic paths, all…

math.CO2026

A note on tree-cycle Ramsey numbers

Ting Huang, Yanbo Zhang, Yaojun Chen

Let denote the Ramsey number of a tree on vertices versus a cycle of length . Burr, Erdős, Faudree, Rousseau, and Schelp (1982) asked for the least…

math.CO2026

Two-block cycles and chromatic number of Hamiltonian digraphs

Ruilin Zheng, Junying Lu, Xiaolin Wang +1

Let and be positive integers. The family consists of all digraphs obtained from two internally vertex-disjoint directed paths of lengths at least and $\e…

math.CO2026

On regular homogeneously traceable nonhamiltonian graphs

Hangdi Chen, Yaojun Chen

A graph is homogeneously traceable if each vertex is an endpoint of a Hamiltonian path. Chartrand, Gould, and Kapoor (1979) proved irregular homogeneously traceable nonhamiltonian…

math.CO2026

Odd covers for complete graphs and complete 3-graphs

Ting Huang, Jiabao Yang, Yaojun Chen

The Graham-Pollak theorem says that one needs at least complete bipartite graphs to cover each edge of a complete graph on vertices exactly once. The odd cover…

math.CO2026

The Turán number of the triangular pyramid of 4-layers

Hangdi Chen, Yaojun Chen, Xiutao Zhu

The Turán number of a graph is the maximum number of edges in any -free graph on vertices. The triangular pyramid of -layers, denoted by , is a genera…