Author

Lu-Jia Wang

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Preprint Sep 2026

Balanced even cycles in signed graphs:Tur\'an bounds, double covers, and parity obstructions

We study Tur\'an problems for balanced even cycles in simple signed graphs, where signed subgraphs are considered up to switching. For every balanced bipartite signed graph, the signed and ordinary Tur\'an numbers differ by at most a factor of two. Our main structural results concern the underlying graphs that admit a...

Lu-Jia Wang, Xiao-Wei Yu · 0 citations

Preprint Sep 2026

Obstructions to coloring arithmetic graphs

The arithmetic graph $B_n$ joins distinct $a,b\in\N$ when $\max(a,b)/\gcd(a,b)\le n$. We prove $\chi(B_{205})=206$, disproving the conjecture that $\chi(B_n)=n$ for every $n$, equivalently the Rainbow Cascades Conjecture. The proof reduces an arbitrary tiling by the arithmetic exponent tile to a periodic tiling, then t...

Lu-Jia Wang, Rui-Hua Wang · 0 citations