Quantum photonic computing chips and its algorithms by Zhu, Huihui

“…The GBS-based quantum photonic microprocessor is applied to solve task assignment, Boolean satisfiability, graph clique, max cut, and vertex cover. These demonstrations suggest an excellent benchmarking platform, paving the way toward large-scale combinatorial optimization. …”
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The Differential on Graph Operator Q(G) by Ludwin A. Basilio, Jair Castro Simon, Jesús Leaños, Omar Rosario Cayetano

“…Besides, we exhibit some results relating the differential <inline-formula> <math display="inline"> <semantics> <mrow> <mi>∂</mi> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> and well-known graph invariants, such as the domination number, the independence number, and the vertex-cover number.…”
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The bidimensionality theory and its algorithmic applications by Hajiaghayi, MohammadTaghi

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Effectiveness and design of sparse process flexibilities by Wei, Yehua, Ph. D. Massachusetts Institute of Technology

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From the Quasi-Total Strong Differential to Quasi-Total Italian Domination in Graphs by Abel Cabrera Martínez, Alejandro Estrada-Moreno, Juan Alberto Rodríguez-Velázquez

“…</mo></mrow></semantics></math></inline-formula> We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. …”
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An algorithm to compute primary decomposition of monomial ideals equigenerated in degree 2 by Giancarlo Rinaldo

“…We give an algorithm to compute primary decomposition of monomial ideals equigenerated in degree 2 and establish connections with minimal vertex covers of a simple graph. We also describe an implementation in C++ of the algorithm.…”
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Confidential Greedy Graph Algorithm by Daniel Waszkiewicz, Aleksandra Horubała, Piotr Sapiecha, Michał Andrzejczak

“…Confidential algorithm for the approximate graph vertex covering problem is presented in this article. …”
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FPT algorithms to recognize well covered graphs by Rafael Araujo, Eurinardo Costa, Sulamita Klein, Rudini Sampaio, Ueverton S. Souza

“…Given a graph $G$, let $vc(G)$ and $vc^+(G)$ be the sizes of a minimum and a maximum minimal vertex covers of $G$, respectively. We say that $G$ is well covered if $vc(G)=vc^+(G)$ (that is, all minimal vertex covers have the same size). …”
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Efficient and safe software defined network topology discovery protocol by Dong LI, Junqing YU, Yongpu GU, Pengcheng ZHAO

“…The network topology discovery in OpenFlow-based software-defined networks is mainly achieved by utilizing the OpenFlow discovery protocol (OFDP).However, it has been observed in existing research that OFDP exhibits low updating efficiency and is susceptible to network topology pollution attacks.To address the efficiency and safety concerns of the network topology discovery protocol, an in-depth investigation was conducted on the mechanism and safety of OFDP network topology discovery.The characteristics of network topology establishment and updating in OFDP were analyzed, and an improved protocol named Im-OFDP (improved OpenFlow discovery protocol) based on the minimum vertex covering problem in graph theory was proposed.In Im-OFDP, the switch port table and network link table were initially established using prior information obtained from OFDP network topology discovery.Subsequently, a graph model of the network topology was constructed, and the minimum vertex covering algorithm in graph theory was employed to select specific switches for the reception and forwarding of topology discovery link layer discovery protocol (LLDP) packets.Multi-level flow tables were designed based on the network topology structure, and these flow entries were installed on the selected switches by the controller to process LLDP packets.To address security issues, dynamic check code verification in LLDP packets was employed to ensure the safety of network links.Additionally, a network equipment information maintenance mechanism was established based on known network topologies to ensure the safety of the network equipment.Experimental results demonstrate a significant reduction in the number of network topology discovery messages, bandwidth overhead, and CPU overhead through the deployment of Im-OFDP.Moreover, the response time for node failures and link recovery time after mode failure is substantially reduced.Im-OFDP also effectively mitigates various network topology pollution attacks, such as link fabrication and switch forgery attacks.Overall, Im-OFDP has the capability to enhance the efficiency and safety of SDN topology discovery.…”
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Rowmotion and generalized toggle groups by Jessica Striker

“…We apply these theorems and find other results on generalized toggle groups in the following settings: chains, antichains, and interval-closed sets of a poset; independent sets, vertex covers, acyclic subgraphs, and spanning subgraphs of a graph; matroids and convex geometries. …”
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Some problems in combinatorial geometry by Oxley, J, Oxley, James G.

“…</p> <p>In Chapter 4 we prove the binary case of a matroid conjecture of Welsh which is a natural analogue of Gallai's theorem that the vertex-stability and vertex-covering numbers of a graph G sum to the number of vertices of G.…”

Direct multiplicative methods for sparse matrices. Newton methods by Anastasiya Borisovna Sviridenko

“…The problem of minimizing a quadratic polynomial is $NP$-hard, since an $NP$-hard problem about a vertex covering for an arbitrary graph comes down to it. …”
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