The Cockayne-Hedetniemi Domination Chain is a chain of inequalities between classic parameters of graph theory: for a given graph G, ir(G) <= gamma(G) <= iota(G) <= alpha(G) <= Gamma(G) <= IR(G). These parameters return the maximum/minimum cardinality of a set satisfying some property. However, they can be generalized for graphs with weighted vertices where the objective is to maximize/minimize the sum of weights of a set satisfying the same property, and the domination chain still holds for them. In this work, the definition of these parameters as well as the chain is formalized in Coq/Ssreflect.
@InProceedings{severin:LIPIcs.ITP.2019.36, author = {Sever{\'\i}n, Daniel E.}, title = {{Formalization of the Domination Chain with Weighted Parameters}}, booktitle = {10th International Conference on Interactive Theorem Proving (ITP 2019)}, pages = {36:1--36:7}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-122-1}, ISSN = {1868-8969}, year = {2019}, volume = {141}, editor = {Harrison, John and O'Leary, John and Tolmach, Andrew}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.36}, URN = {urn:nbn:de:0030-drops-110919}, doi = {10.4230/LIPIcs.ITP.2019.36}, annote = {Keywords: Domination Chain, Coq, Formalization of Mathematics} }
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