On the hardness of recognizing triangular line graphs

The hardness of the independence and matching clutter of a graph

A {\it clutter} (or {\it antichain} or {\it Sperner family}) $L$ is a pair $(V,E)$, where $V$ is a finite set and $E$ is a family of subsets of $V$ none of which is a subset of another. Usually, the elements of $V$ are called {\it vertices} of $L$, and the elements of $E$ are called {\it edges} of $L$. A subset $s_e$ of an edge $e$ of a clutter is called {\it recognizing} for $e$, if $s_e$ is not a subset of another edge. The {\it hardness} of an edge $e$ of a clutter is the ratio of the size of $e\textrm{'s}$ smallest recognizing subset to the size of $e$. The hardness of a clutter is the max…

A tight lower bound for the hardness of clutters

A {\it clutter} (or {\it antichain} or {\it Sperner family}) $L$ is a pair $(V,E)$, where $V$ is a finite set and $E$ is a family of subsets of $V$ none of which is a subset of another. Normally, the elements of $V$ are called {\it vertices} of $L$, and the elements of $E$ are called {\it edges} of $L$. A subset $s_e$ of an edge $e$ of a clutter is {\it recognizing} for $e$, if $s_e$ is not a subset of another edge. The {\it hardness} of an edge $e$ of a clutter is the ratio of the size of $e\textrm{'s}$ smallest recognizing subset to the size of $e$. The hardness of a clutter is the maximum h…

识别小mim宽图的难度及其变体

On the hardness of recognizing graphs of small mim-width and its variants

本文证明了识别小mim宽图及变体问题在NP难，且通过无根四元组一致性问题进行归约。

识别叶幂图与成对相容图是NP完全问题

Recognizing Leaf Powers and Pairwise Compatibility Graphs is NP-Complete

本研究针对叶幂图与成对相容图识别难题，证明二者识别问题均为NP完全，并将该难度结论推广至含多区间成对相容图在内的更广泛图类层级，推进了相关图类性质的研究。

加权图的边复杂度：对合对称性与NP困难性

Edge complexity of weighted graphs: involutory symmetries and NP-hardness

本文研究加权图边复杂度的计算难度，通过添加通用顶点建立与对合对称性的联系，证明其近似计算是NP困难的，并给出NP完全性及非实傅里叶系数的示例。

边分解为两个三角森林是NP完全问题

Edge-decomposition into Two Triangular Forests is NP-complete

研究将图边分解为两个三角森林问题的复杂度，通过考虑满足特定条件的最简单图类三角森林，证明该边分解问题是NP完全的。