Further results on binary codes of covering radius 2 and saturating sets in projective spaces
本文解决了二进制码覆盖半径为2的问题，通过构建新的无限码族和使用不同的q^m-连接构造方法，得到了更优的上界。
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Representative Papers
Reduced polynomial lifts of APN permutations over Galois rings and effective non-APN bounds
该研究解决了APN置换在Galois环上的提升问题，通过使用归约多项式表示和Janwa-Wilson-Rodier曲面方法，证明了特定条件下不存在APN函数，并给出了具体的阈值。
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Extending Biconnected Straight-Line Planar Drawings
This study addresses the Partial Drawing Extensibility (PDE) problem for planar graphs when the initial partial drawing is biconnected. By leveraging graph embedding analysis, complexity reductions, and the Existential Theory of the Reals (ETR), the authors establish for the first time that PDE remains NP-hard even when the given subgraph is biconnected and the input graph is subcubic. On the algorithmic side, they devise a polynomial-time algorithm running in $O(p^2 n)$ time under a fixed embedding and develop a fixed-parameter tractable (FPT) algorithm parameterized by the vertex cover number. This work delineates the computational complexity landscape of PDE in the biconnected setting and achieves efficient solutions under fixed embeddings and path-extension constraints.
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On the Recognition of Outerplanar Graphs with Queue Number 1
This study addresses the decision problem of whether an outerplanar graph admits a queue number of one. We prove that this problem is NP-hard for general outerplanar graphs, yet it can be solved efficiently in linear time $O(n)$ for maximal outerplanar graphs. Through a combination of graph-theoretic analysis and computational complexity theory, we uncover an intrinsic relationship between outerpaths with queue number one and their maximum vertex degree. Our work establishes, for the first time, the precise complexity boundary for recognizing queue-number-one outerplanar graphs and provides an optimal recognition algorithm for the maximal case.
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Stack and Queue Layouts with Defects
Traditional stack and queue layouts require edge sets to be entirely non-crossing or non-nested, which severely restricts the classes of graphs they can handle. This work proposes a *k*-defective stack/queue layout model that permits each edge to cross (in stacks) or nest (in queues) with at most *k* other edges within the same set, thereby substantially relaxing these constraints while preserving the linear layout structure. Through combinatorial graph-theoretic analysis and algorithmic design, the study systematically investigates the existence, upper and lower bounds, and constructive methods for such layouts across various graph classes. The results extend the theory of linear layouts and establish, for the first time, a quantitative relationship between the complexity and expressive power of defective layouts.
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Further results on binary codes of covering radius 2 and saturating sets in projective spaces
本文解决了二进制码覆盖半径为2的问题，通过构建新的无限码族和使用不同的q^m-连接构造方法，得到了更优的上界。
0 citationsRead paper
Reduced polynomial lifts of APN permutations over Galois rings and effective non-APN bounds
该研究解决了APN置换在Galois环上的提升问题，通过使用归约多项式表示和Janwa-Wilson-Rodier曲面方法，证明了特定条件下不存在APN函数，并给出了具体的阈值。
0 citationsRead paper
Extending Biconnected Straight-Line Planar Drawings
This study addresses the Partial Drawing Extensibility (PDE) problem for planar graphs when the initial partial drawing is biconnected. By leveraging graph embedding analysis, complexity reductions, and the Existential Theory of the Reals (ETR), the authors establish for the first time that PDE remains NP-hard even when the given subgraph is biconnected and the input graph is subcubic. On the algorithmic side, they devise a polynomial-time algorithm running in $O(p^2 n)$ time under a fixed embedding and develop a fixed-parameter tractable (FPT) algorithm parameterized by the vertex cover number. This work delineates the computational complexity landscape of PDE in the biconnected setting and achieves efficient solutions under fixed embeddings and path-extension constraints.
0 citationsRead paper
On the Recognition of Outerplanar Graphs with Queue Number 1
This study addresses the decision problem of whether an outerplanar graph admits a queue number of one. We prove that this problem is NP-hard for general outerplanar graphs, yet it can be solved efficiently in linear time $O(n)$ for maximal outerplanar graphs. Through a combination of graph-theoretic analysis and computational complexity theory, we uncover an intrinsic relationship between outerpaths with queue number one and their maximum vertex degree. Our work establishes, for the first time, the precise complexity boundary for recognizing queue-number-one outerplanar graphs and provides an optimal recognition algorithm for the maximal case.
0 citationsRead paper
Stack and Queue Layouts with Defects
Traditional stack and queue layouts require edge sets to be entirely non-crossing or non-nested, which severely restricts the classes of graphs they can handle. This work proposes a *k*-defective stack/queue layout model that permits each edge to cross (in stacks) or nest (in queues) with at most *k* other edges within the same set, thereby substantially relaxing these constraints while preserving the linear layout structure. Through combinatorial graph-theoretic analysis and algorithmic design, the study systematically investigates the existence, upper and lower bounds, and constructive methods for such layouts across various graph classes. The results extend the theory of linear layouts and establish, for the first time, a quantitative relationship between the complexity and expressive power of defective layouts.
0 citationsRead paper