@InProceedings{block_et_al:LIPIcs.ITC.2021.16, author = {Block, Alexander R. and Br\^{a}nzei, Simina and Maji, Hemanta K. and Mehta, Himanshi and Mukherjee, Tamalika and Nguyen, Hai H.}, title = {{P₄-free Partition and Cover Numbers \& Applications}}, booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)}, pages = {16:1--16:25}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-197-9}, ISSN = {1868-8969}, year = {2021}, volume = {199}, editor = {Tessaro, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.16}, URN = {urn:nbn:de:0030-drops-143357}, doi = {10.4230/LIPIcs.ITC.2021.16}, annote = {Keywords: Secure keys, Secure private randomness, Gray-Wyner system, Cryptographic complexity, Nondeterministic communication complexity, Leakage-resilience, Combinatorial optimization, Product dimension, Zarankiewicz problem, Algebraic lower-bounding techniques, P₄-free partition number, P₄-free cover number} }