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European Journal of Combinatorics, ISSN 0195-6698, 02/2014, Volume 36, pp. 231 - 236
For k≥2, let H be a k-uniform hypergraph on n vertices and m edges. The transversal number τ(H) of H is the minimum number of vertices that intersect every... 
MATHEMATICS | SYSTEMS | MATCHINGS | INTERSECTION THEOREMS | TOTAL DOMINATION | FINITE SETS | GRAPHS | Linearity | Combinatorial analysis
Journal Article
Discrete Mathematics, ISSN 0012-365X, 04/2016, Volume 339, Issue 4, pp. 1355 - 1361
In this paper we consider upper bounds on the diameter of Eulerian digraphs containing a vertex of large degree. Define the maximum degree of a digraph to be... 
Maximum degree | Digraph | Diameter | Distance | Eulerian digraph | MATHEMATICS | Upper bounds | Mathematical analysis | Graph theory
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 217, pp. 506 - 511
We show that the total domination number of a maximal outerplanar graph G is bounded above by n+k3, where n is the order of G and k is the number of vertices... 
Domination | Outerplanar graph | Total domination | PLANAR GRAPHS | MATHEMATICS, APPLIED | SETS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 03/2016, Volume 339, Issue 3, pp. 1180 - 1188
The total domination number of a graph is the minimum size of a set S such that every vertex has a neighbor in S. We show that a maximal outerplanar graph of... 
Domination | Outerplanar graph | Total domination | MATHEMATICS | THEOREM | SETS | PLANAR GRAPHS
Journal Article
by Rebbeck, Timothy R and Friebel, Tara M and Friedman, Eitan and Hamann, Ute and Huo, Dezheng and Kwong, Ava and Olah, Edith and Olopade, Olufunmilayo I and Solano, Angela R and teo, Soo-Hwang and Thomassen, Mads and Weitzel, Jeffrey N and Chan, T. L and Couch, Fergus J and Goldgar, David E and Kruse, Torben A and Palmero, Edenir Inêz and Park, Sue Kyung and Torres, Diana and van Rensburg, Elizabeth J and McGuffog, Lesley and Parsons, Michael T and Leslie, Goska and Aalfs, Cora M and Abugattas, Julio and Adlard, Julian and Agata, Simona and Aittomäki, Kristiina and Anews, Lesley and Anulis, Irene L and Arason, Adalgeir and Arnold, Norbert and Arun, Banu K and Asseryanis, Ella and Auerbach, Leo and Azzollini, Jacopo and Balmaña, Judith and Barile, Monica and Barkardottir, Rosa B and Barrowdale, Daniel and Benitez, Javier and Berger, Aneas and Berger, Raanan and Blanco, Amie M and Blazer, Kathleen R and Blok, Marinus J and Bonadona, Valérie and Bonanni, Bernardo and Bradbury, Angela R and Brewer, Carole and Buecher, Bruno and Buys, Sauna S and Caldes, Trinidad and Caliebe, Almuth and Caligo, Maria A and Campbell, Ian and Caputo, Sanine and Chiquette, Jocelyne and Chung, Wendy K and Claes, Kathleen B. M and Collée, J. Margriet and Cook, Jackie and Davidson, Rosemarie and de la Hoya, Miguel and de Leeneer, Kim and de Pauw, Antoine and Delnatte, Capucine and Diez, Orland and Ding, Yuan Chun and Ditsch, Nina and Domchek, Susan M and Dorfling, Cecilia M and Velazquez, Carolina and Dworniczak, Bernd and Eason, Jacqueline and Easton, Douglas F and Eeles, Ros and Ehrencrona, Hans and Ejlertsen, Bent and Engel, Christoph and Engert, Stefanie and Evans, D. Gareth and Faivre, Laurence and Feliubadaló, Lidia and Ferrer, Sana Fert and Foretova, Lenka and Fowler, Jeffrey and Frost, Debra and Galvão, Henrique C. R and Ganz, Patricia A and Garber, Judy and Gauthier-Villars, Marion and Gehrig, Anea and Gerdes, Anne-Marie and Gesta, Paul and Giannini, Giuseppe and Giraud, Sophie and Glendon, Gord and Godwin, Anew K and Greene, Mark H and ... and KConFab Investigators and HEBON and EMBRACE and GEMO Study Collaborators
Human mutation, ISSN 1059-7794, 2018, Volume 39, Issue 5, pp. 593 - 620
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 16, pp. 2491 - 2497
A property of graphs is a non-empty isomorphism-closed class of simple graphs. If P1,…,Pn are properties of graphs, the property P1∘⋯∘Pn is the class of all... 
Additive | Graph property | Hereditary | Factorization | Decomposability | MATHEMATICS | Graphs | Partitions | Decomposition | Mathematical analysis
Journal Article
Jnci-Journal of the national cancer institute, ISSN 0027-8874, 07/2017, Volume 109, Issue 7, p. djw302
Journal Article
by Meeks, Huong D and Song, Honglin and Michailidou, Kyriaki and Bolla, Manjeet and Dennis, Joe and Wang, Qing and Barrowdale, Daniel and Frost, Debra and McGuffog, Lesley and Ellis, Steve and Feng, Bingjian and Buys, Sauna and Hopper, John and Southey, Melissa and Tesoriero, Anea and James, Margaret and Bruinsma, Fiona and Campbell, Ian and Broeks, Annegien and Schmidt, Marjanka and Hogervorst, Frans and Beckmann, Matthias and Fasching, Peter and Fletcher, Olivia and Johnson, Nichola and Sawyer, Elinor and Riboli, Elio and Banerjee, Susana and Menon, Usha and Tomlinson, Ian and Burwinkel, Barbara and Hamann, Ute and Marme, Federick and Rudolph, Anja and Janavicius, Ramunas and Tihomirova, Laima and Tung, Nadine and Garber, Judy and Cramer, Daniel and Terry, Kathryn and Poole, Elizabeth and Tworoger, Shelley and Dorfling, Cecilia and Rensburg, Elizabeth and Godwin, Anew K and Guénel, Pascal and Truong, Thérèse and Stoppa-Lyonnet, Dominique and Damiola, Francesca and Mazoyer, Sylvie and Sinilnikova, Olga and Isaacs, Claudine and Maugard, C and Bojesen, Stig and Flyger, Henrik and Gerdes, Anne-Marie and Hansen, Thomas and Jensen, Allen and Kjaer, Michael and Høgdall, Claus and Høgdall, Estrid and Pedersen, Inge Sokilde and Thomassen, Mads and Benítez, Javier and González-Neira, Anna and Osorio, Ana and Hoya, Miguel De La and Segura, Peo Perez and Díez, Orland and Lázaro, Conxi and Brunet, Joan and Anton-Culver, Hoda and Eunjung, Lee and John, Esther and Neuhausen, Susan and Ding, Yuan and Castillo, Danielle and Weitzel, Jeffrey and Ganz, Patricia A and Nussbaum, Robert and Chan, Salina and Karlan, Beth Y and Lester, Kathryn and Wu, Anna and Gayther, Simon and Ramus, Susan and Sieh, Weiva and Whittermore, Alice S and Monteiro, Alvaro N.A and Phelan, Catherine and Terry, Mary Beth and Piedmonte, Marion and Offit, Kenneth and Robson, Mark and Levine, Douglas and Moysich, Kirsten B and Cannioto, Rikki and Olson, Sara and Daly, Mary B and Nathanson, Katherine and ... and kConFab Investigators and EMBRACE and GEMO Study Collaborators and Australia Ovarian Canc Study Grp and PRostate Canc Assoc Grp and HEBON and OCGN and PRostate cancer AssoCiation group To Investigate Cancer Associated aLterations in the genome and Australia Ovarian Cancer Study Group
National Cancer Institute. Journal (Print), ISSN 0027-8874, 02/2016, Volume 108, Issue 2, p. djv315
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2006, Volume 154, Issue 6, pp. 1023 - 1027
The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex... 
Power domination | Grid | power domination | MATHEMATICS, APPLIED | grid | Electric power systems
Journal Article
Discussiones Mathematicae - Graph Theory, ISSN 1234-3099, 2012, Volume 32, Issue 1, pp. 81 - 90
For a graph G and a vertex-coloring c : V(G) -> {1, 2,..., k}, the color code of a vertex v is the (k 1)-tuple (a(0), a(1),, a(k)), where a(0) = c(v), and for... 
Recognition number | Recognizable coloring | MATHEMATICS | recognition number | recognizable coloring
Journal Article
by Milne, Roger L and Kuchenbaecker, Karoline B and Michailidou, Kyriaki and Beesley, Jonathan and Kar, Siddhartha and Lindström, Sara and Hui, Shirley and Lemaçon, Auey and Soucy, Penny and Dennis, Joe and Jiang, Xia and Rostamianfar, Asha and Finucane, Hilary and Bolla, Manjeet K and McGuffog, Lesley and Wang, Qin and Aalfs, Cora M and Adams, Marcia and Adlard, Julian and Agata, Simona and Ahmed, Shahana and Ahsan, Habibul and Aittomäki, Kristiina and Al-Ejeh, Fares and Allen, Jamie and Ambrosone, Christine B and Amos, Christopher I and Anulis, Irene L and Anton-Culver, Hoda and Antonenkova, Natalia N and Arndt, Volker and Arnold, Norbert and Aronson, Kristan J and Auber, Bernd and Auer, Paul L and Ausems, Margreet G. E. M and Azzollini, Jacopo and Bacot, François and Balmaña, Judith and Barile, Monica and Barjhoux, Laure and Barkardottir, Rosa B and Barrdahl, Myrto and Barnes, Daniel and Barrowdale, Daniel and Baynes, Caroline and Beckmann, Matthias W and Benitez, Javier and Bermisheva, Marina and Bernstein, Leslie and Bignon, Yves-Jean and Blazer, Kathleen R and Blok, Marinus J and Blomqvist, Carl and Blot, William and Bobolis, Kristie and Boeckx, Bram and Bogdanova, Natalia V and Bojesen, Anders and Bojesen, Stig E and Bonanni, Bernardo and Børresen-Dale, Anne-Lise and Bozsik, Aniko and Bradbury, Angela R and Brand, Judith S and Brauch, Hiltrud and Brenner, Hermann and Bressac-de Paillerets, Brigitte and Brewer, Carole and Brinton, Louise and Broberg, Per and Brooks-Wilson, Angela and Brunet, Joan and Brüning, Thomas and Burwinkel, Barbara and Buys, Sauna S and Byun, Jinyoung and Cai, Qiuyin and Caldés, Trinidad and Caligo, Maria A and Campbell, Ian and Canzian, Federico and Caron, Olivier and Carracedo, Angel and Carter, Brian D and Castelao, J. Esteban and Castera, Laurent and Caux-Moncoutier, Virginie and Chan, Salina B and Chang-Claude, Jenny and Chanock, Stephen J and Chen, Xiaoqing and Cheng, Ting-Yuan David and Chiquette, Jocelyne and Christiansen, Hans and Claes, Kathleen B. M and Clarke, Christine L and Conner, Thomas and Conroy, Don M and Cook, Jackie and ... and ABCTB Investigators and HEBON and EMBRACE and GEMO Study Collaborators and kConFab AOCS Investigators and NBSC Collaborators and kConFab/AOCS Investigators and Medicinska fakulteten and Medicinska och farmaceutiska vetenskapsområdet and Institutionen för immunologi, genetik och patologi and Medicinsk genetik och genomik and Ortopedi and Uppsala universitet and Institutionen för kirurgiska vetenskaper
Nature genetics, ISSN 1061-4036, 2017, Volume 49, Issue 12, pp. 1767 - 1778
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 6/2012, Volume 119, Issue 6, pp. 502 - 506
A divisibility condition, together with some kind of boundedness, ensure that a function : ℤ → ℤ is a polynomial function. 
Integers | NOTES | Mathematical theorems | Maps | Applied mathematics | Polynomials | Mathematical functions | Division | Mathematical congruence | Curvature | MATHEMATICS | Numbers, Natural | Theorems (Mathematics) | Analysis | Tests, problems and exercises
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2013, Volume 313, Issue 19, pp. 1961 - 1964
An additive hereditary graph property is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If P1,…,Pn are graph properties,... 
Graph property | Decomposable property | MATHEMATICS
Journal Article
by Zeng, Chenjie and Guo, X and Long, Jirong and Kuchenbaecker, Karoline and it, Arnaud and Michailidou, Kyriaki and Ghoussaini, Maya and Kar, Siddhartha and Freeman, A and Hopper, John and Milne, Roger and Bolla, Manjeet K and Wang, Q and Dennis, Joe and Agata, Simona and Ahmed, Shahana and Aittomäki, Kristiina and Anulis, Irene and Anton-Culver, Hoda and Antonenkova, N.N and Arason, Adalgeir and Arndt, V and Arun, Banu and Arver, Brita Wasteson and Bacot, Francois and Barrowdale, Daniel and Baynes, C and Beeghly-Fadiel, Alicia and Benítez, Javier and Bermisheva, Marina and Blomqvist, Carl and Blot, William and Bogdanova, Natalia and Bojesen, Stig and Bonnani, Bernardo and Borresen-Dale, Anne-Lise and Brand, Judith S and Brauch, Hiltrud and Brennan, Paul and Brenner, Hermann and Broeks, Annegien and Brüning, Thomas and Burwinkel, Barbara and Buys, Sauna and Cai, Qiuyin and Caldes, Trinidad and Campbell, Ian and Carpenter, Aian and Chang-Claude, Jenny and Choi, J.-Y and Claes, Kathleen B.M and Clarke, Christine and Cox, Angela and Cross, Simon and Czene, Kamila and Daly, Mary B and Hoya, Miguel and De Leeneer, Kim and Devilee, Peter and Díez, Orland and Domchek, Susan and Doody, Michele and Dorfling, Cecilia and Dörk, Thilo and Santos Silva, Isabel and Dumont, Martine and Dwek, Miriam and Dworniczak, B and Egan, Kathleen and Eilber, Ursula and Einbeigi, Zakaria and Ejlertsen, Bent and Ellis, Steve and Frost, Debra and Lalloo, Fiona and Fasching, Peter and Figueroa, Jonine and Flyger, Henrik and Friedlander, Michael and Friedman, Eitan and Gambino, G and Gao, Y.-T and Garber, Judy and García-Closas, Montserrat and Gehrig, Paola A and Damiola, Francesca and Lesueur, Fabienne and Mazoyer, Sylvie and Stoppa-Lyonnet, Dominique and Giles, G.G and Godwin, Anew K and Goldgar, David and González-Neira, Anna and Greene, Mark H and Guénel, Pascal and Haeberle, Lothar and Haiman, Christopher A and Hallberg, E and Hamann, Ute and Hansen, Thomas and ... and AOCS Investigators and KConFab and HEBON and EMBRACE and GEMO Study Collaborators and behalf of GEMO Study Collaborators and on behalf of HEBON and on behalf of KConFab and on behalf of EMBRACE and Medicinska fakulteten and Medicinska och farmaceutiska vetenskapsområdet and Institutionen för immunologi, genetik och patologi and Uppsala universitet
Breast Cancer Research (Print), ISSN 1465-5411, 06/2016, Volume 18, Issue 1, p. 64
Journal Article