@article{ORCA,
	author = {Neese,F.},
	title = {The ORCA program system},
	journal = {WIRES Comput. Molec. Sci.},
	volume = {2},
	number = {1},
	pages = {73-78},
	DOI = {10.1002/wcms.81},
	year = {2012},
	type = {journal Article}
}
@article{DFTORCA,
	author = {Neese, Frank and Wennmohs, Frank and Becker, Ute and Riplinger, Christoph},
	title = {The ORCA quantum chemistry program package},
	journal = {The Journal of Chemical Physics},
	volume = {152},
	number = {22},
	pages = {224108},
	year = {2020},
	month = {06},
	abstract = {In this contribution to the special software-centered issue, the ORCA program package is described. We start with a short historical perspective of how the project began and go on to discuss its current feature set. ORCA has grown into a rather comprehensive general-purpose package for theoretical research in all areas of chemistry and many neighboring disciplines such as materials sciences and biochemistry. ORCA features density functional theory, a range of wavefunction based correlation methods, semi-empirical methods, and even force-field methods. A range of solvation and embedding models is featured as well as a complete intrinsic to ORCA quantum mechanics/molecular mechanics engine. A specialty of ORCA always has been a focus on transition metals and spectroscopy as well as a focus on applicability of the implemented methods to “real-life” chemical applications involving systems with a few hundred atoms. In addition to being efficient, user friendly, and, to the largest extent possible, platform independent, ORCA features a number of methods that are either unique to ORCA or have been first implemented in the course of the ORCA development. Next to a range of spectroscopic and magnetic properties, the linear- or low-order single- and multi-reference local correlation methods based on pair natural orbitals (domain based local pair natural orbital methods) should be mentioned here. Consequently, ORCA is a widely used program in various areas of chemistry and spectroscopy with a current user base of over 22 000 registered users in academic research and in industry.},
	issn = {0021-9606},
	doi = {10.1063/5.0004608},
	url = {https://doi.org/10.1063/5.0004608},
	eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/5.0004608/16740678/224108_1_online.pdf},
}
@misc{ Nobody06,
	author = "Nobody Jr",
	title = "My Article",
	year = "2006" } 

@book{bender2006foundations,
	title={Foundations of Combinatorics with Applications},
	author={Bender, Edward A. and Williamson, S. Gill},
	year={2006},
	publisher={Dover Publications},
	address={Mineola, NY},
	edition={Dover},
	pages={468},
	isbn={978-0486446035},
	note={ISBN-10: 0-486-44603-4}
}
@book{
	Graphtheory,
	title = {Graphentheorie : eine anwendungsorientierte Einführung},
	series = {Mathematik-Studienhilfen},
	author = {Tittmann, Peter},
	address = {München},
	publisher = {Hanser},
	year = {2019},
	edition = {3., aktualisierte Auflage},
	url = {https://doi.org/10.3139/9783446465039},
	url = {https://www.hanser-elibrary.com/doi/book/10.3139/9783446465039},
}
@article{andersenhyperflow,
	author = {Andersen, Jakob L. and Flamm, Christoph and Merkle, Daniel and Stadler, Peter F.},
	title = {Chemical Transformation Motifs—Modelling Pathways as Integer Hyperflows},
	year = {2019},
	issue_date = {March-April 2019},
	publisher = {IEEE Computer Society Press},
	address = {Washington, DC, USA},
	volume = {16},
	number = {2},
	issn = {1545-5963},
	url = {https://doi.org/10.1109/TCBB.2017.2781724},
	doi = {10.1109/tcbb.2017.2781724},
	abstract = {We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and hyperedges to reactions. Pathways are modelled as integer hyperflows and we expand the network model by detailed routing constraints. In contrast to the more traditional approaches like Flux Balance Analysis or Elementary Mode analysis we insist on integer-valued flows. While this choice makes it necessary to solve possibly hard integer linear programs, it has the advantage that more detailed mechanistic questions can be formulated. It is thus possible to query networks for general transformation motifs, and to automatically enumerate optimal and near-optimal pathways. Similarities and differences between our work and traditional approaches in metabolic network analysis are discussed in detail. To demonstrate the applicability of the mathematical framework to real-life problems we first explore the design space of possible non-oxidative glycolysis pathways and show that recent manually designed pathways can be further optimized. We then use a model of sugar chemistry to investigate pathways in the autocatalytic formose process. A graph transformation-based approach is used to automatically generate the reaction networks of interest.},
	journal = {IEEE/ACM Trans. Comput. Biol. Bioinformatics},
	month = apr,
	pages = {510–523},
	numpages = {14}
}
@book{ocwiley,
	author    = {K. Peter, C. Vollhardt, Neil E. Schore},
	title     = {Organische Chemie},
	publisher = {Wiley-VCH},
	year      = {2020},
	isbn      = {978-3-527-34582-3},
}
@phdthesis{andersenphd,
	title        = {Analysis of Generative Chemistries},
	author       = {    Jakob Lykke Andersen },
	year         = 2015,
	month        = {September},
	address      = {Leipzig, DE},
	note         = {Available at \url{    https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa-202723}},
	school       = {Universität Leipzig},
	type         = {PhD thesis}
}
@book{equilibrium,
	title={Principles of organic synthesis},
	author={Norman, Richard OC},
	year={2017},
	publisher={Routledge}
}
@article{lewisrep,
	author = {Packer, John E. and Woodgate, Sheila D.},
	title = {Lewis structures, formal charge, and oxidation numbers: A more user-friendly approach},
	journal = {Journal of Chemical Education},
	volume = {68},
	number = {6},
	pages = {456-456},
	year = {1991},
	month = {06},
	abstract = {This paper presents a set of rules for writing Lewis structures requiring only the ability to add, subtract, count, and know the number of valence electrons of neutral atoms.},
	issn = {0021-9584},
	doi = {10.1021/ed068p456},
	url = {https://doi.org/10.1021/ed068p456},
	eprint = {https://pubs.acs.org/jceda8/article-pdf/68/6/456/416109/ed068p456.pdf},
}
@article{hypergraphpath,
	author = {Spencer Krieger and John Kececioglu},
	title ={Shortest Hyperpaths in Directed Hypergraphs for Reaction Pathway Inference},
	
	journal = {Journal of Computational Biology},
	volume = {30},
	number = {11},
	pages = {1198-1225},
	year = {2023},
	doi = {10.1089/cmb.2023.0242},
	
	URL = { 
	
	
	https://journals.sagepub.com/doi/abs/10.1089/cmb.2023.0242
	
	
	},
	eprint = { 
	
	
	https://journals.sagepub.com/doi/pdf/10.1089/cmb.2023.0242
	
	
	}
	,
	abstract = { Signaling and metabolic pathways, which consist of chains of reactions that produce target molecules from source compounds, are cornerstones of cellular biology. Properly modeling the reaction networks that represent such pathways requires directed hypergraphs, where each molecule or compound maps to a vertex, and each reaction maps to a hyperedge directed from its set of input reactants to its set of output products. Inferring the most likely series of reactions that produces a given set of targets from a given set of sources, where for each reaction its reactants are produced by prior reactions in the series, corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete.We give the first exact algorithm for general shortest hyperpaths that can find provably optimal solutions for large, real-world, reaction networks. In particular, we derive a novel graph-theoretic characterization of hyperpaths, which we leverage in a new integer linear programming formulation of shortest hyperpaths that for the first time handles cycles, and develop a cutting-plane algorithm that can solve this integer linear program to optimality in practice. Through comprehensive experiments over all of the thousands of instances from the standard Reactome and NCI-PID reaction databases, we demonstrate that our cutting-plane algorithm quickly finds an optimal hyperpath—inferring the most likely pathway—with a median running time of under 10 seconds, and a maximum time of less than 30 minutes, even on instances with thousands of reactions. We also explore for the first time how well hyperpaths infer true pathways, and show that shortest hyperpaths accurately recover known pathways, typically with very high precision and recall.Source code implementing our cutting-plane algorithm for shortest hyperpaths is available free for research use in a new tool called Mmunin. }
}
@ARTICLE{chordlesscycle,
	author = {{Silva Dias}, Elis{\^a}ngela and {Castonguay}, Diane and {Longo}, Humberto and {Abdala Rfaei Jradi}, Walid},
	title = "{Efficient Enumeration of Chordless Cycles}",
	journal = {arXiv e-prints},
	keywords = {Computer Science - Data Structures and Algorithms, Computer Science - Discrete Mathematics},
	year = 2013,
	month = sep,
	eid = {arXiv:1309.1051},
	pages = {arXiv:1309.1051},
	doi = {10.48550/arXiv.1309.1051},
	archivePrefix = {arXiv},
	eprint = {1309.1051},
	primaryClass = {cs.DS},
	adsurl = {https://ui.adsabs.harvard.edu/abs/2013arXiv1309.1051S},
	adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@inbook{ilp,
	publisher = {John Wiley & Sons, Ltd},
	isbn = {9781118166000},
	title = {Linear Programming—Fundamentals},
	booktitle = {Applied Integer Programming},
	doi = {https://doi.org/10.1002/9781118166000},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118166000},
	eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118166000},
	year = {2009},
	keywords = {traveling salesman problem, Hamiltonian paths, machine sequencing problems, vehicle Routing, genome sequencing},
}
@article{petrinets,
	author = {Peterson, James L.},
	title = {Petri Nets},
	year = {1977},
	issue_date = {Sept. 1977},
	publisher = {Association for Computing Machinery},
	address = {New York, NY, USA},
	volume = {9},
	number = {3},
	issn = {0360-0300},
	url = {https://doi.org/10.1145/356698.356702},
	doi = {10.1145/356698.356702},
	journal = {ACM Comput. Surv.},
	month = sep,
	pages = {223–252},
	numpages = {30}
}
@book{atkinsdft,
	abstract = {This text unravels those fundamental physical principles which explain how all matter behaves. It takes us from the foundations of quantum mechanics, through quantum models of atomic, molecular, and electronic structure, and on to discussions of spectroscopy, and the electronic and magnetic properties of molecules.},
	author = {Atkins, P. W. and Friedman, R. S.},
	address = {Oxford},
	booktitle = {Molecular quantum mechanics},
	edition = {5th ed. / Peter Atkins and Ronald Friedman.},
	isbn = {9780199541423},
	keywords = {Quantum chemistry ; Science},
	language = {eng},
	publisher = {Oxford University Press},
	title = {Molecular quantum mechanics },
	year = {2011},
}