Author

Chang Liu

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Preprint Aug 2026

Unbalanced Tur\'an and spectral Tur\'an problems with prescribed large maximum degree

Classical Tur\'an theory shows that, without additional constraints, the extremal structure of $F$-free graphs is governed by the chromatic number of $F$ and is asymptotically the balanced Tur\'an graph. We investigate how prescribing a large maximum degree changes this picture and leads to an unbalanced Tur\'an proble...

Chang Liu · 1 citation

Preprint Sep 2026

Unbalanced spectral Tur\'an problem for color-critical graphs with prescribed large maximum degree

Let $F$ be a connected color-critical graph with $\chi(F)=r+1\ge4$, let $S_{n,\Delta}^{(r)}=(n-\Delta)K_1\vee T(\Delta,r-1)$. We determine the graph of maximum adjacency spectral radius among all $n$-vertex $F$-free graphs with prescribed maximum degree $\Delta$. There is a constant $s_F\in[0,1)$ such that, for all suf...

Chang Liu · 1 citation