Abstract
Stephen Hedetniemi is perhaps best known for his pioneering work in domination in graphs. In this chapter, we explore some of his contributions to the direction and advancement of this field of study. We focus on two topics, namely domination of chessboard graphs and the domination chain.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S. Arumugam, S.T. Hedetniemi, S.M. Hedetniemi, L. Sathikala, S. Sudha, The covering chain of a graph. Util. Math. 98, 183–196 (2015)
W.W. Rouse Ball, Mathematical Recreations and Essays, revision by H.S.M. Coxeter of the original 1892; Minimum Pieces Problem, 3rd edn. (Macmillan, London, 1939)
C. Berge, Theory of Graphs and Its Applications (Methuen, London, 1962)
W. Bird, Computational Methods for Domination Problems. Doctoral Dissertation, University of Victoria, 2017
B. Bollobás, E.J. Cockayne, Graph theoretic parameters concerning domination, independence and irredundance. J. Graph Theory 3, 241–250 (1979)
S. Bozóki, P. Gál, I. Marosi W.D. Weakley, Domination of the rectangular queens graph, submitted
M. Chellali, T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, A. McRae, A Roman domination chain. Graphs Comb. 32, 79–92 (2016)
E.J. Cockayne, R.M. Dawes, S.T. Hedetniemi, Total domination in graphs. Networks 10, 211–219 (1980)
E.J. Cockayne, O. Favaron, C. Payan, A. Thomason, Contributions to the theory of domination, independence, and irredundance in graphs. Discret. Math. 33, 249–258 (1981)
E.J. Cockayne, J.H. Hattingh, S.M. Hedetniemi, S.T. Hedetniemi, A.A. McRae, Using maximality and minimality conditions to construct inequality chains. Discret. Math. 176, 43–61 (1997)
E.J. Cockayne, S.T. Hedetniemi, On the diagonal queens domination problem. J. Comb. Theory Ser. A 42, 137–139 (1986)
E.J. Cockayne, S.T. Hedetniemi, D.J. Miller, Properties of hereditary hypergraphs and middle graphs. Canad. Math. Bull. 21, 461–468 (1978)
C.F. De Jaenisch, Applications de I’Analyse Mathematique an Jeu des Echecs (Petrograd, 1863)
D. Finozhenok, W.D. Weakley, An improved lower bound for domination numbers of the queen’s graph. Australas. J. Comb. 37, 295–300 (2007)
G.H. Fricke, S.M. Hedetniemi, S.T. Hedetniemi, A. McRae, C.K. Wallis, M.S. Jacobson, H.W. Martin, W.D. Weakley, Combinatorial problems on chessboards: a brief survey. Graph Theory, Combinatorics, and Algorithms, vol. 1, 2 (Kalamazoo, 1992), pp. 507–528; (Wiley-Interscience Publication, Wiley, New York, 1995)
T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998)
S.M. Hedetniemi, S.T. Hedetniemi, R. Reynolds, Combinatorial problems on chessboards. II, Domination in Graphs, Monographs and Textbooks in Pure and Applied Mathematics, vol. 209 (Dekker, New York, 1998), pp. 133–162
S.T. Hedetniemi, My top 10 graph theory conjectures and open problems, in Graph Theory, Favorite Conjectures and Open Problems, Volume 1, ed. by R. Gera, S.T. Hedetniemi, C. Larson (Springer, Berlin, 2018), pp. 177–281
D. König, Theorie der endlichen und unendlichen graphen (Akademische Verlagsgesellschaft M.B.H. Leipzig, 1936) and (Chelsea Publishing, New York, 1950)
P.R.J. Östergård, W.D. Weakley, Values of domination numbers of the queen’s graph. Electron. J. Comb. 8 (2001), Research Paper 29, 19 pp
A. Sinko, P.J. Slater, Queens domination using border squares and (A, B)-restricted domination. Discret. Math. 308, 4822–4828 (2008)
W.D. Weakley, A lower bound for domination numbers of the queen’s graph. J. Comb. Math. Comb. Comput. 43, 231–254 (2002)
W.D. Weakley, Upper bounds for domination numbers of the queen’s graph. Discret. Math. 242, 229–243 (2002)
W.D. Weakley, Domination in the queen’s graph, Graph Theory, Combinatorics, and Algorithms, vol. 1, 2 (Kalamazoo, 1992), pp. 1223–1232; (Wiley-Interscience Publication, Wiley, New York, 1995)
W.D. Weakley, Queens around the world in twenty-five years, in Graph Theory, Favorite Conjectures and Open Problems, Volume 2, ed. by R. Gera, T.W. Haynes, S.T. Hedetniemi (Springer, Berlin, 2018), pp. 43–54
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Chartrand, G., Haynes, T.W., Henning, M.A., Zhang, P. (2019). Pioneer of Domination in Graphs. In: From Domination to Coloring. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-31110-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-030-31110-0_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-31109-4
Online ISBN: 978-3-030-31110-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)