Author

Xin-Yuan Li

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Preprint Sep 2026

Bounded chromatic number of graphs with small clique number and large minimum degree

We prove that every triangle-free graph with minimum degree at least $\frac{n}{3}$ is $4$-colorable and thereby settle a problem of Brandt and Thomass\'e (2005) at the threshold $\frac{n}{3}$. The number four is best possible. For a positive integer-valued function $f(n)=o(n)$, we relate the chromatic number of $f(n)$-...

Jia-Ao Li, Xin-Yuan Li · 0 citations

Open access Sep 2026

Circular Flows of Random Regular Graphs With Large Valency

For positive integers with , a circular ‐flow of a graph is defined as a pair where represents an orientation of , and is a function mapping the edges of to the set such that, at each vertex, the sum of the ‐values of the incoming edges equals the sum of the ‐values of the outgoing edges. The flow index of , denoted...

Jia-Ao Li, Xin-Yuan Li · Journal of Graph Theory · 0 citations