Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. Packings in bipartite prisms and hypercubes. (English) Zbl 07806404 Discrete Math. 347, No. 4, Article ID 113875, 6 p. (2024). MSC: 05C70 05C15 05C69 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Math. 347, No. 4, Article ID 113875, 6 p. (2024; Zbl 07806404) Full Text: DOI arXiv
Bacsó, Gábor; Brešar, Boštjan; Kuenzel, Kirsti; Rall, Douglas F. Graphs with equal Grundy domination and independence number. (English) Zbl 1514.05117 Discrete Optim. 48, Part 2, Article ID 100777, 15 p. (2023). MSC: 05C69 05C75 PDFBibTeX XMLCite \textit{G. Bacsó} et al., Discrete Optim. 48, Part 2, Article ID 100777, 15 p. (2023; Zbl 1514.05117) Full Text: DOI arXiv
Anderson, Sarah; Brešar, Boštjan; Klavžar, Sandi; Kuenzel, Kirsti; Rall, Douglas F. Orientable domination in product-like graphs. (English) Zbl 1510.05227 Discrete Appl. Math. 326, 62-69 (2023). Reviewer: Seyed Mahmood Sheikholeslami (Tabriz) MSC: 05C69 05C20 05C76 PDFBibTeX XMLCite \textit{S. Anderson} et al., Discrete Appl. Math. 326, 62--69 (2023; Zbl 1510.05227) Full Text: DOI arXiv
Brešar, Boštjan; Kuenzel, Kirsti; Rall, Douglas F. Domination in digraphs and their direct and Cartesian products. (English) Zbl 07746117 J. Graph Theory 99, No. 3, 359-377 (2022). MSC: 05C20 05C69 05C76 PDFBibTeX XMLCite \textit{B. Brešar} et al., J. Graph Theory 99, No. 3, 359--377 (2022; Zbl 07746117) Full Text: DOI arXiv
Brešar, Boštjan; Pandey, Arti; Sharma, Gopika Computational aspects of some vertex sequences of Grundy domination-type. (English) Zbl 1495.05212 Indian J. Discrete Math. 8, No. 1, 21-38 (2022). MSC: 05C69 05C65 PDFBibTeX XMLCite \textit{B. Brešar} et al., Indian J. Discrete Math. 8, No. 1, 21--38 (2022; Zbl 1495.05212) Full Text: Link
Brešar, Boštjan; Brezovnik, Simon Grundy domination and zero forcing in regular graphs. (English) Zbl 1479.05248 Bull. Malays. Math. Sci. Soc. (2) 44, No. 6, 3637-3661 (2021). Reviewer: Eunjeong Yi (Galveston) MSC: 05C69 05C35 PDFBibTeX XMLCite \textit{B. Brešar} and \textit{S. Brezovnik}, Bull. Malays. Math. Sci. Soc. (2) 44, No. 6, 3637--3661 (2021; Zbl 1479.05248) Full Text: DOI arXiv
Brešar, Boštjan; Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. Domination games played on graphs. (English) Zbl 1467.91015 SpringerBriefs in Mathematics. Cham: Springer (ISBN 978-3-030-69086-1/pbk; 978-3-030-69087-8/ebook). x, 121 p. (2021). Reviewer: Vasile Postolică (Piatra Neamţ) MSC: 91A43 05C57 91A18 05C69 05C65 PDFBibTeX XMLCite \textit{B. Brešar} et al., Domination games played on graphs. Cham: Springer (2021; Zbl 1467.91015) Full Text: DOI
Brešar, Boštjan; Hartnell, Bert L.; Henning, Michael A.; Kuenzel, Kirsti; Rall, Douglas F. A new framework to approach Vizing’s conjecture. (English) Zbl 1459.05231 Discuss. Math., Graph Theory 41, No. 3, 749-762 (2021). MSC: 05C69 05C76 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discuss. Math., Graph Theory 41, No. 3, 749--762 (2021; Zbl 1459.05231) Full Text: DOI
Brešar, Boštjan; Bujtás, Csilla; Gologranc, Tanja; Klavžar, Sandi; Košmrlj, Gašper; Marc, Tilen; Patkós, Balázs; Tuza, Zsolt; Vizer, Máté On Grundy total domination number in product graphs. (English) Zbl 1453.05085 Discuss. Math., Graph Theory 41, No. 1, 225-247 (2021). MSC: 05C69 05C76 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discuss. Math., Graph Theory 41, No. 1, 225--247 (2021; Zbl 1453.05085) Full Text: DOI arXiv
Brešar, Boštjan; Gologranc, Tanja; Henning, Michael A.; Kos, Tim On the L-Grundy domination number of a graph. (English) Zbl 1499.05448 Filomat 34, No. 10, 3205-3215 (2020). MSC: 05C69 05C65 05C85 PDFBibTeX XMLCite \textit{B. Brešar} et al., Filomat 34, No. 10, 3205--3215 (2020; Zbl 1499.05448) Full Text: DOI
Brešar, Boštjan Rainbow domination in graphs. (English) Zbl 1479.05247 Haynes, Teresa W. (ed.) et al., Topics in domination in graphs. Cham: Springer. Dev. Math. 64, 411-443 (2020). MSC: 05C69 05C15 PDFBibTeX XMLCite \textit{B. Brešar}, Dev. Math. 64, 411--443 (2020; Zbl 1479.05247) Full Text: DOI Euclid
Brešar, Boštjan; Henning, Michael A. A \(\frac{3}{4}\)-approximation of Vizing’s conjecture for claw-free graphs. (English) Zbl 1443.05138 Discrete Appl. Math. 284, 416-422 (2020). MSC: 05C69 05C76 PDFBibTeX XMLCite \textit{B. Brešar} and \textit{M. A. Henning}, Discrete Appl. Math. 284, 416--422 (2020; Zbl 1443.05138) Full Text: DOI
Brešar, Boštjan; Kos, Tim; Torres, Pablo Daniel Grundy domination and zero forcing in Kneser graphs. (English) Zbl 1433.05244 Ars Math. Contemp. 17, No. 2, 419-430 (2019). MSC: 05C69 05C76 05D05 PDFBibTeX XMLCite \textit{B. Brešar} et al., Ars Math. Contemp. 17, No. 2, 419--430 (2019; Zbl 1433.05244) Full Text: DOI
Brešar, Boštjan; Bujtás, Csilla; Gologranc, Tanja; Klavžar, Sandi; Košmrlj, Gašper; Marc, Tilen; Patkós, Balázs; Tuza, Zsolt; Vizer, Máté The variety of domination games. (English) Zbl 1428.05218 Aequationes Math. 93, No. 6, 1085-1109 (2019). MSC: 05C57 05C69 91A43 91A05 PDFBibTeX XMLCite \textit{B. Brešar} et al., Aequationes Math. 93, No. 6, 1085--1109 (2019; Zbl 1428.05218) Full Text: DOI arXiv Link
Brešar, Boštjan; Movarraei, Nazanin On the number of maximal independent sets in minimum colorings of split graphs. (English) Zbl 1394.05057 Discrete Appl. Math. 247, 352-356 (2018). MSC: 05C30 05C69 05C15 PDFBibTeX XMLCite \textit{B. Brešar} and \textit{N. Movarraei}, Discrete Appl. Math. 247, 352--356 (2018; Zbl 1394.05057) Full Text: DOI
Brešar, Boštjan; Kos, Tim; Nasini, Graciela; Torres, Pablo Total dominating sequences in trees, split graphs, and under modular decomposition. (English) Zbl 1462.05272 Discrete Optim. 28, 16-30 (2018). MSC: 05C69 05C85 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Optim. 28, 16--30 (2018; Zbl 1462.05272) Full Text: DOI arXiv Link
Brešar, Boštjan; Hartinger, Tatiana Romina; Kos, Tim; Milanič, Martin On total domination in the Cartesian product of graphs. (English) Zbl 1392.05086 Discuss. Math., Graph Theory 38, No. 4, 963-976 (2018). MSC: 05C69 05C76 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discuss. Math., Graph Theory 38, No. 4, 963--976 (2018; Zbl 1392.05086) Full Text: DOI arXiv
Brešar, Boštjan; Gologranc, Tanja; Kos, Tim Convex and isometric domination of (weak) dominating pair graphs. (English) Zbl 1391.05195 Theor. Comput. Sci. 730, 32-43 (2018). MSC: 05C69 68Q17 05C85 PDFBibTeX XMLCite \textit{B. Brešar} et al., Theor. Comput. Sci. 730, 32--43 (2018; Zbl 1391.05195) Full Text: DOI arXiv
Bonomo, Flavia; Brešar, Boštjan; Grippo, Luciano N.; Milanič, Martin; Safe, Martín D. Domination parameters with number 2: interrelations and algorithmic consequences. (English) Zbl 1375.05193 Discrete Appl. Math. 235, 23-50 (2018). MSC: 05C69 PDFBibTeX XMLCite \textit{F. Bonomo} et al., Discrete Appl. Math. 235, 23--50 (2018; Zbl 1375.05193) Full Text: DOI arXiv Link
Brešar, Boštjan; Bujtás, Csilla; Gologranc, Tanja; Klavžar, Sandi; Košmrlj, Gašper; Patkós, Balázs; Tuza, Zsolt; Vizer, Máté Grundy dominating sequences and zero forcing sets. (English) Zbl 1387.05177 Discrete Optim. 26, 66-77 (2017). MSC: 05C69 05C65 05C85 68Q25 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Optim. 26, 66--77 (2017; Zbl 1387.05177) Full Text: DOI arXiv Link
Brešar, Boštjan Improving the Clark-Suen bound on the domination number of the Cartesian product of graphs. (English) Zbl 1367.05155 Discrete Math. 340, No. 10, 2398-2401 (2017). MSC: 05C69 05C76 PDFBibTeX XMLCite \textit{B. Brešar}, Discrete Math. 340, No. 10, 2398--2401 (2017; Zbl 1367.05155) Full Text: DOI
Brešar, Boštjan; Henning, Michael A. The game total domination problem is log-complete in PSPACE. (English) Zbl 1409.68133 Inf. Process. Lett. 126, 12-17 (2017). MSC: 68Q25 05C57 05C69 68Q17 PDFBibTeX XMLCite \textit{B. Brešar} and \textit{M. A. Henning}, Inf. Process. Lett. 126, 12--17 (2017; Zbl 1409.68133) Full Text: DOI
Brešar, Boštjan; Dorbec, Paul; Klavžar, Sandi; Košmrlj, Gašper How long can one bluff in the domination game? (English) Zbl 1359.05081 Discuss. Math., Graph Theory 37, No. 2, 337-352 (2017). MSC: 05C57 91A43 91A05 05C69 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discuss. Math., Graph Theory 37, No. 2, 337--352 (2017; Zbl 1359.05081) Full Text: DOI
Brešar, Boštjan; Gologranc, Tanja; Kos, Tim Dominating sequences under atomic changes with applications in Sierpiński and interval graphs. (English) Zbl 1461.05152 Appl. Anal. Discrete Math. 10, No. 2, 518-531 (2016). MSC: 05C69 05C85 PDFBibTeX XMLCite \textit{B. Brešar} et al., Appl. Anal. Discrete Math. 10, No. 2, 518--531 (2016; Zbl 1461.05152) Full Text: DOI arXiv
Brešar, Boštjan; Bujtás, Csilla; Gologranc, Tanja; Klavžar, Sandi; Košmrlj, Gašper; Patkós, Balázs; Tuza, Zsolt; Vizer, Máté Dominating sequences in grid-like and toroidal graphs. (English) Zbl 1353.05105 Electron. J. Comb. 23, No. 4, Research Paper P4.34, 19 p. (2016). MSC: 05C76 05C69 PDFBibTeX XMLCite \textit{B. Brešar} et al., Electron. J. Comb. 23, No. 4, Research Paper P4.34, 19 p. (2016; Zbl 1353.05105) Full Text: arXiv Link
Brešar, Boštjan; Dorbec, Paul; Klavžar, Sandi; Košmrlj, Gašper; Renault, Gabriel Complexity of the game domination problem. (English) Zbl 1350.68131 Theor. Comput. Sci. 648, 1-7 (2016). MSC: 68Q25 05C57 05C69 68Q17 PDFBibTeX XMLCite \textit{B. Brešar} et al., Theor. Comput. Sci. 648, 1--7 (2016; Zbl 1350.68131) Full Text: DOI arXiv
Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. Total dominating sequences in graphs. (English) Zbl 1333.05214 Discrete Math. 339, No. 6, 1665-1676 (2016). MSC: 05C69 05C12 05C35 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Math. 339, No. 6, 1665--1676 (2016; Zbl 1333.05214) Full Text: DOI arXiv
Brešar, Boštjan Vizing’s conjecture for graphs with domination number 3 – a new proof. (English) Zbl 1323.05099 Electron. J. Comb. 22, No. 3, Research Paper P3.38, 8 p. (2015). MSC: 05C69 05C76 PDFBibTeX XMLCite \textit{B. Brešar}, Electron. J. Comb. 22, No. 3, Research Paper P3.38, 8 p. (2015; Zbl 1323.05099) Full Text: Link
Brešar, Boštjan; Rall, Douglas F. On Cartesian products having a minimum dominating set that is a box or a stairway. (English) Zbl 1327.05255 Graphs Comb. 31, No. 5, 1263-1270 (2015). MSC: 05C69 PDFBibTeX XMLCite \textit{B. Brešar} and \textit{D. F. Rall}, Graphs Comb. 31, No. 5, 1263--1270 (2015; Zbl 1327.05255) Full Text: DOI
Brešar, Boštjan; Klavžar, Sandi; Košmrlj, Gasper; Rall, Doug F. Guarded subgraphs and the domination game. (English) Zbl 1311.05123 Discrete Math. Theor. Comput. Sci. 17, No. 1, 161-168 (2015). MSC: 05C57 05C69 05C60 91A43 91A05 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Math. Theor. Comput. Sci. 17, No. 1, 161--168 (2015; Zbl 1311.05123) Full Text: Link
Brešar, Boštjan; Gologranc, Tanja; Milanič, Martin; Rall, Douglas F.; Rizzi, Romeo Dominating sequences in graphs. (English) Zbl 1300.05210 Discrete Math. 336, 22-36 (2014). MSC: 05C69 05C65 68Q17 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Math. 336, 22--36 (2014; Zbl 1300.05210) Full Text: DOI
Brešar, Boštjan; Dorbec, Paul; Klavžar, Sandi; Košmrlj, Gašper Domination game: effect of edge- and vertex-removal. (English) Zbl 1295.05152 Discrete Math. 330, 1-10 (2014). MSC: 05C57 05C69 05C60 91A43 91A05 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Math. 330, 1--10 (2014; Zbl 1295.05152) Full Text: DOI arXiv
Brešar, Boštjan; Klavžar, Sandi; Košmrlj, Gašper; Rall, Douglas F. Domination game: extremal families of graphs for \(3/5\)-conjectures. (English) Zbl 1287.05088 Discrete Appl. Math. 161, No. 10-11, 1308-1316 (2013). MSC: 05C57 05C69 68R10 68P10 91A43 91A05 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Appl. Math. 161, No. 10--11, 1308--1316 (2013; Zbl 1287.05088) Full Text: DOI
Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. Domination game played on trees and spanning subgraphs. (English) Zbl 1262.05104 Discrete Math. 313, No. 8, 915-923 (2013). MSC: 05C57 05C05 05C60 05C69 91A43 91A05 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Math. 313, No. 8, 915--923 (2013; Zbl 1262.05104) Full Text: DOI arXiv
Brešar, Boštjan; Dorbec, Paul; Goddard, Wayne; Hartnell, Bert L.; Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. Vizing’s conjecture: a survey and recent results. (English) Zbl 1234.05173 J. Graph Theory 69, No. 1-2, 46-76 (2012). MSC: 05C69 05C76 PDFBibTeX XMLCite \textit{B. Brešar} et al., J. Graph Theory 69, No. 1--2, 46--76 (2012; Zbl 1234.05173) Full Text: DOI
Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. Domination game and an imagination strategy. (English) Zbl 1223.05189 SIAM J. Discrete Math. 24, No. 3, 979-991 (2010). MSC: 05C57 91A43 05C69 05C76 PDFBibTeX XMLCite \textit{B. Brešar} et al., SIAM J. Discrete Math. 24, No. 3, 979--991 (2010; Zbl 1223.05189) Full Text: DOI Link
Brešar, Boštjan; Špacapan, Simon Broadcast domination of products of graphs. (English) Zbl 1224.05359 Ars Comb. 92, 303-320 (2009). MSC: 05C69 05C12 PDFBibTeX XMLCite \textit{B. Brešar} and \textit{S. Špacapan}, Ars Comb. 92, 303--320 (2009; Zbl 1224.05359)
Brešar, Boštjan; Rall, Douglas F. Fair reception and Vizing’s conjecture. (English) Zbl 1179.05080 J. Graph Theory 61, No. 1, 45-54 (2009). MSC: 05C69 PDFBibTeX XMLCite \textit{B. Brešar} and \textit{D. F. Rall}, J. Graph Theory 61, No. 1, 45--54 (2009; Zbl 1179.05080) Full Text: DOI
Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. Rainbow domination in graphs. (English) Zbl 1163.05046 Taiwanese J. Math. 12, No. 1, 213-225 (2008). MSC: 05C69 05C15 PDFBibTeX XMLCite \textit{B. Brešar} et al., Taiwanese J. Math. 12, No. 1, 213--225 (2008; Zbl 1163.05046) Full Text: DOI
Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. Paired-domination of Cartesian products of graphs. (English) Zbl 1161.05053 Util. Math. 73, 255-265 (2007). Reviewer: Ambat Vijayakumar (Cochin) MSC: 05C69 05C70 PDFBibTeX XMLCite \textit{B. Brešar} et al., Util. Math. 73, 255--265 (2007; Zbl 1161.05053)
Brešar, Boštjan; Šumenjak, Tadeja Kraner On the 2-rainbow domination in graphs. (English) Zbl 1126.05091 Discrete Appl. Math. 155, No. 17, 2394-2400 (2007). MSC: 05C85 05C69 PDFBibTeX XMLCite \textit{B. Brešar} and \textit{T. K. Šumenjak}, Discrete Appl. Math. 155, No. 17, 2394--2400 (2007; Zbl 1126.05091) Full Text: DOI
Brešar, Bostjan; Klavžar, Sandi; Rall, Douglas F. Dominating direct products of graphs. (English) Zbl 1116.05055 Discrete Math. 307, No. 13, 1636-1642 (2007). Reviewer: Mikhail Ostrovskii (Queens) MSC: 05C69 05C12 PDFBibTeX XMLCite \textit{B. Brešar} et al., Discrete Math. 307, No. 13, 1636--1642 (2007; Zbl 1116.05055) Full Text: DOI
Brešar, Boštjan; Henning, Michael A.; Klavžar, Sandi On integer domination in graphs and Vizing-like problems. (English) Zbl 1109.05081 Taiwanese J. Math. 10, No. 5, 1317-1328 (2006). Reviewer: Lutz Volkmann (Aachen) MSC: 05C69 PDFBibTeX XMLCite \textit{B. Brešar} et al., Taiwanese J. Math. 10, No. 5, 1317--1328 (2006; Zbl 1109.05081) Full Text: DOI
Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. Paired-domination of Cartesian products of graphs and rainbow domination. (English) Zbl 1200.05154 Raspaud, André (ed.) et al., 7th international colloquium on graph theory, Hyeres, France, September 12–16, 2005. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 22, 233-237 (2005). MSC: 05C69 05C76 05C15 PDFBibTeX XMLCite \textit{B. Brešar} et al., Electron. Notes Discrete Math. 22, 233--237 (2005; Zbl 1200.05154) Full Text: DOI
Brešar, Boštjan On Vizing’s conjecture. (English) Zbl 0989.05084 Discuss. Math., Graph Theory 21, No. 1, 5-11 (2001). MSC: 05C69 PDFBibTeX XMLCite \textit{B. Brešar}, Discuss. Math., Graph Theory 21, No. 1, 5--11 (2001; Zbl 0989.05084) Full Text: DOI Link