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Zhiguo Li

Publications and source records attributed to Zhiguo Li.

18 recordsLinked to original sources
arXiv2026

Partial Petrial Polynomials of Bouquets

Gross, Mansour, and Tucker [European J. Combin., 95 (2021): 103329] introduced the \emph{partial Petrial polynomial} of a ribbon graph $G$, denoted by $^{\partial}{\varepsilon^{\times}_G}(z)$. For a prime bouquet $B_n$, Yan and Li [Discrete Appl. Math., 375 (2025): 281-289] determined $^{\partial}{\varepsilon^{\times}_{B_n}}(z)$ when the intersection graph $I(B_n)$ is either the complete graph or a path, and provided an equivalent condition under which the lowest degree of the nonzero coefficient in $^{\partial}{\varepsilon^{\times}_{B_n}}(z)$ is $1$. In this paper, we determine $^{\partial}{\varepsilon^{\times}_{B_n}}(z)$ when the intersection graph is a cycle. Moreover, we present a complete characterization of the prime bouquets whose lowest nonzero term in $^{\partial}{\varepsilon^{\times}_{B_n}}(z)$ is of degree $2$ and determine the partial Petrial polynomial for the prime bouquets. As corollaries, we determine $^{\partial}{\varepsilon^{\times}_{B_n}}(z)$ when $I(B_n)$ is the complete bipartite and tripartite graph.

math.CO↗
arXiv2026

Partial Petrial Polynomials of Ribbon Graphs

Gross, Mansour, and Tucker [European J. Combin., 95 (2021): 103329] introduced the \emph{partial Petrial polynomial} of a ribbon graph $G$, denoted by $^{\partial}{\varepsilon^{\times}_{G}}(z)$. Beck and Mellor proved, in both orientable and non-orientable cases respectively, that the Euler genus of a bouquet equals the rank of a certain matrix over $\mathbb{GF}(2)$. In this paper, we first generalize Beck and Mellor's results from bouquets to all ribbon graphs. Secondly, we give an equivalent representation of the partial Petrial polynomial for all ribbon graphs. Specifically, the partial Petrial polynomial of a ribbon graph $G$ with $n$ vertices is equal to the sum of this polynomial for $2^{n-1}$ distinct bouquets. Moreover, we give the definition of a modified partial Petrial polynomial by assigning coefficients $+1$ or $-1$ to the terms in the partial Petrial polynomial such that the resulting polynomial satisfies the four-term relation for graphs. Finally, we generalize the modified partial Petrial polynomial from bouquets to all signed simple graphs and prove that this polynomial is $4$-invariant, which provides an answer to the problem posed by Lando [J.~Combin.~Theory Ser.~B,~80~(1) (2000): 104-121]: Which of the known graph invariants are $4$-invariants?

math.CO↗
arXiv2026

The matching book embedding of the $F$-sum of two graphs

The $F$-sum is a new graph operation defined by combining four graph transformation operations with the Cartesian product operation. A matching book embedding of a graph $G$ is a book embedding in which the vertices of $G$ are placed on a fixed linear order along the spine, and the edges are assigned to pages such that (i) no two edges on the same page cross, and (ii) each vertex has degree at most one on every page. The minimum number of pages required for such a matching book embedding is called the \emph{matching book thickness} of $G$, denoted by $mbt(G)$. A graph $G $ is dispersable if and only if $ mbt(G) = \Delta(G) $, and nearly dispersable if and only if $mbt(G) = \Delta(G) + 1 $. In this paper, we determine the dispersability of outerplanar graphs and establish an upper bound on the matching book thickness of the $F$-sum of any simple graph with any dispersable bipartite graph.

math.CO↗
arXiv2026

The degeneracy and Alon-Tarsi number under $F$-sum operations

The Alon-Tarsi number of a graph $ G $ is the smallest $ k $ such that there exists an orientation $ D $ of $ G $ with maximum outdegree $ k - 1 $ satisfying that the number of even Eulerian subgraphs is different from the number of odd Eulerian subgraphs. The degeneracy of a graph $ G $ is the maximum value of the minimum degree over all subgraphs of $ G $. In this paper, we obtain a characterization of graphs with $AT(G)=2$ for any graph $G$, and study the Alon-Tarsi number of $F$-sum in terms of degeneracy.

math.CO↗
arXiv2025

The Alon-Tarsi Number of Cartesian product and Corona product of Hypercube Graph and Special Graphs

The \emph{Alon-Tarsi number} of a graph $G$ is the smallest $k$ so that there exists an orientation $D$ of $G$ with max outdegree $k-1$ satisfying the number of even Eulerian subgraphs different from the number of odd Eulerian subgraphs. In this paper, the Alon-Tarsi number of the $n$-cube is obtained according to its special properties, we obtain the Alon-Tarsi number of Cartesian product of some special bipartite graphs, and get the Alon-Tarsi number of Corona product of graphs. As corollaries, we get the Alon-Tarsi number of Cartesian product and Corona product of hypercube graph and special graphs.

math.CO↗
arXiv2024

A note on the Nearly Dispersability of Odd Toroidal Grids

The \emph{matching book thickness} $mbt(G)$ of $G$ is the minimum integer $m$ such that an $m$-page matching book embedding exists. A graph $G$ is called \emph{dispersable} if $mbt(G)=\Delta(G)$, \emph{nearly dispersable} if $mbt(G)=\Delta(G)+1$. Recently, the authors determined the nearly dispersability of odd toroidal grids $T_{s,t}$. In this note, we further present a brief proof for this result.

math.CO↗
arXiv2024

On the dispersability of graph bundles over cycles

In this paper, the dispersability of the Cartesian graph bundle over two cycles is completely solved. We show the Cartesian graph bundle $G$ over two cycles is dispersable if $G$ is bipartite; otherwise, $G$ is nearly dispersable.

math.CO↗
arXiv2023

Highly Efficient SNNs for High-speed Object Detection

The high biological properties and low energy consumption of Spiking Neural Networks (SNNs) have brought much attention in recent years. However, the converted SNNs generally need large time steps to achieve satisfactory performance, which will result in high inference latency and computational resources increase. In this work, we propose a highly efficient and fast SNN for object detection. First, we build an initial compact ANN by using quantization training method of convolution layer fold batch normalization layer and neural network modification. Second, we theoretically analyze how to obtain the low complexity SNN correctly. Then, we propose a scale-aware pseudoquantization scheme to guarantee the correctness of the compact ANN to SNN. Third, we propose a continuous inference scheme by using a Feed-Forward Integrate-and-Fire (FewdIF) neuron to realize high-speed object detection. Experimental results show that our efficient SNN can achieve 118X speedup on GPU with only 1.5MB parameters for object detection tasks. We further verify our SNN on FPGA platform and the proposed model can achieve 800+FPS object detection with extremely low latency.

cs.CV↗
arXiv2022

Matching Book Thickness of Halin Graphs

The \emph{matching book embedding} of a graph $G$ is to arrange its vertices on the spine, and draw its edges into the pages so that the edges on every page do not intersect each other and the maximum degree of vertices on every page is one. The \emph{matching book thickness} is the minimum number of pages in which the graph $G$ can be matching embedded. In this paper, the matching book thickness of Halin graphs is determined.

math.CO↗
arXiv2022

The Matching Book Embedding of Biconnected Outerplanar Graphs

The $n$-$book ~embedding$ of a graph $G$ is an embedding of the graph $G$ in an $n$-book with the vertices of $G$ on the spine and each edge to the pages without crossing each other. If the degree of vertices of $G$ at most one in each page, the $n$-book embedding is $matching$. The $matching~ book~ thickness$ of graph $G$ is the smallest $n$ so that $G$ can be matching embedded in an $n$-book. In this paper, the matching book thickness of the biconnected outerplanar graphs is determined.

math.CO↗
arXiv2021

The Alon-Tarsi number of Halin graphs

The Alon-Tarsi number of a graph $G$ is the smallest $k$ for which there is an orientation $D$ of $G$ with max outdegree $k-1$ such that the number of Eulerian subgraphs of $G$ with an even number of edges differs from the number of Eulerian subgraphs with an odd number of edges. In this paper, we obtain the Alon-Tarsi number of a Halin graph equals 4 when it is a wheel of even order and 3 otherwise.

math.CO↗
arXiv2021

Bipartite cubic planar graphs are dispersable

The book embedding of a graph $G$ is to place the vertices of $G$ on the spine and draw the edges to the pages so that the edges in the same page do not cross with each other. A book embedding is matching if the vertices in the same page have maximum degree at most 1. The matching book thickness is the minimum number of pages in which a graph can be matching book embedded. A graph $G$ is dispersable if and only if $mbt(G)=Δ(G)$. In this paper, we prove that bipartite cubic planar graphs are dispersable.

math.CO↗
arXiv2020

Embedding the Complete Expansion Graph in Books

A book embedding of a graph consists of an embedding of its vertices along the spine of a book, and an embedding of its edges on the pages such that edges embedded on the same page do not intersect. The pagenumber is the minimum number of pages in which the graph $G$ can be embedded. The main purpose of this paper is to study the book embedding of the complete expansion graph. This is the first work about it, and some exact pagenumbers of the complete expansion graphs of some special graphs are obtained.

math.CO↗
arXiv2020

Matching Book Embedding of the Cartesian Product of a Complete Graph and a Cycle

The $book$ $embedding$ of a graph $G$ is to place the vertices of $G$ on the spine and draw the edges to the pages so that the edges in the same page do not cross with each other. The book embedding is $matching$ if the pages have maximum degree $1$. The $matching$ $book$ $thickness$ is the minimum number of pages in which graphs can be matching book embedded. In this paper, we show that the matching book thickness of the Cartesian product $K_p\Box C_q$of a complete graph $K_p$ and a cycle $C_q$ is equal to $Δ(K_p\Box C_q)+1$.

math.CO↗
arXiv2019

The Alon-Tarsi Number of A Toroidal Grid

The Alon-Tarsi number $AT(G)$ of a graph $G$ is the smallest $k$ for which there is an orientation $D$ of $G$ with max indegree $k-1$ such that the number of even and odd circulations contained in D are different. In this paper, we show that the Alon--Tarsi number of toroidal grids $T_{m,n}=C_m\Box C_n$ equals $4$ when $m,n$ are both odd and $3$ otherwise.

math.CO↗
arXiv2016

Solving the "Magic Angle" Challenge in Determining Molecular Orientation at Interfaces

We introduce a novel method to determine the orientation heterogeneity (mean tilt angle and orientational distribution) of molecules at interfaces using heterodyne two-dimensional sum frequency generation spectroscopy. By doing so, we not only have solved the long-standing "magic angle" challenge, i.e. the measurement of molecular orientation by assuming a narrow orientational distribution results in ambiguities, but we also are able to determine the orientational distribution, which is otherwise difficult to measure. We applied our new method to a CO2 reduction catalyst/gold interface and found that the catalysts formed a monolayer with a mean tilt angle between the quasi-C3 symmetric axis of the catalysts and the surface normal of 53 deg, with 5 deg orientational distribution. Although applied to a specific system, this method is a general way to determine the orientation heterogeneity of an ensemble-averaged molecular interface, which can potentially be applied to a wide-range of energy material, catalytic and biological interfaces.

physics.chem-ph↗
arXiv2013

BigDataBench: a Big Data Benchmark Suite from Web Search Engines

This paper presents our joint research efforts on big data benchmarking with several industrial partners. Considering the complexity, diversity, workload churns, and rapid evolution of big data systems, we take an incremental approach in big data benchmarking. For the first step, we pay attention to search engines, which are the most important domain in Internet services in terms of the number of page views and daily visitors. However, search engine service providers treat data, applications, and web access logs as business confidentiality, which prevents us from building benchmarks. To overcome those difficulties, with several industry partners, we widely investigated the open source solutions in search engines, and obtained the permission of using anonymous Web access logs. Moreover, with two years' great efforts, we created a sematic search engine named ProfSearch (available from http://prof.ict.ac.cn). These efforts pave the path for our big data benchmark suite from search engines---BigDataBench, which is released on the web page (http://prof.ict.ac.cn/BigDataBench). We report our detailed analysis of search engine workloads, and present our benchmarking methodology. An innovative data generation methodology and tool are proposed to generate scalable volumes of big data from a small seed of real data, preserving semantics and locality of data. Also, we preliminarily report two case studies using BigDataBench for both system and architecture researches.

cs.IR↗