K. Brooks Reid
Founding Faculty
Professor
Department of Mathematics, CSUSM

Ph.D., Mathematics, University of Illinois, 1968
M.S., Mathematics, University of Illinois, 1966
B.A., Mathematics,  University of California, Berkeley, 1964

Research interests: combinatorics and graph theory, particularly tournament theory, centrality and anticentrality in graphs, and aspects of voting theory.

rd_pin.gif (1016 bytes)Office: 315 Science Hall 2
rd_pin.gif (1016 bytes)Phone: 760-750-4088
rd_pin.gif (1016 bytes)Fax: 760-750-3439
rd_pin.gif (1016 bytes)Email: breid@csusm.edu
rd_pin.gif (1016 bytes)Address: Department of Mathematics        
    California State University San Marcos     
    San Marcos, CA 92096-0001 USA

currently on sabbatical leave for AY 2002-2003

Administrative Coordinator for Mathematics:
Carrie Huntington  310 Science Hall 2, Phone 760-750-8059, Fax 760-750-3439.

Research Papers  

  1. On sets of arcs containing no cycle in a tournament, Canadian Math.  Bull., 12 (1969), 261-264.

  2. Connectivity in products of graphs, SIAM J. Appl. Math.  18 (1970), 644-651.

  3. Two applications of Turan's theorem to asymmetric digraphs, Combinatorial Structures and Their Applications, Gordon and Breech, New York, (1970), 351-353.

  4. A polyonimoe labeling problem, Congressus Numerantium 1, Utilitas Mathematica, Winnipeg (1970), 227-248.

  5. Disproof of a conjecture of Erdös and Moser on tournaments (with E.T. Parker), J. Comb. Theory 9 (1970), 225-238.

  6. Sequences with adjacent elements unequal (with L.Q. Eifler and D.P. Roselle), Aequationes Mathematica 6 (1971), 256-262.

  7. Edge sets generated by symmetric difference (with L.T. Ollmann), Congressus Numerantium 3, Utilitas Mathematica, Winnipeg (1971), 411-456.

  8. l-cycles in n-tournaments having no k-cycles, ibid., 473-482.

  9. Doubly regular tournaments are equivalent to skew Hadamard matrices (with E. Brown), J. Comb. Theory 12 (1972), 332-338.

  10. On hypotraceable graphs, Congressus Numerantium 6, Utilitas Mathematica, Winnipeg (1972), 409-422.

  11. Equivalence of n-tournaments via k-path reversals, Discrete Math. 6 (1973), 263-280.

  12. The number of graphs on n vertices with 3 cliques, J. London Math. Soc. 8 (1974), 94-98.

  13. Bypasses in asymmetric digraphs (with B. Alspach and D.P. Roselle), J. Comb. Theory B 17 (1974), 11-18.

  14. Sequences with nonrecurring pairs, Congressus Numerantium 10, Utilitas Mathematica, Winnipeg (1974), 599-606.

  15. Mutually disjoint families of 0-1 sequences (with B. Alspach and L.T. Ollman), Discrete Math. 12 (1975), 205-209.

  16. Cycles in the complement of a tree, Discrete Math. 15 (1976), 163-174.

  17. Edge sets contained in circuits (with C. Thomassen), Israel J. Math. 24 (1976), 305-319.

  18.   Strongly self-complementary and hereditarily isomorphic tournaments (with C. Thomassen), Monatsheft für Math. 81 (1976), 291-304.

  19. Representation of permutations as products of cycles of fixed length (with M. Herzog), J. Australian Math. Soc. 22 (1976), 321-331.

  20. Number of factors in k-cycle decompositions of permutations (with M. Herzog), Combinatorial Mathematics IV, Adelaide 1975, Springer-Verlag Lecture Notes in Mathematics 560 (1976), 123-131.

  21. Extension of graphical sequences, Utilitas Math. 12 (1977), 255-261.

  22. Permutation groups generated by cycles of fixed lengths (with M. Herzog), Israel J. Math. 26 (1977), 221-231.

  23. Separating n-systems of sets (with C. Cordes), Congressus Numerantium 14, Utilitas Mathematica, Winnipeg (1977), 183-200.

  24. Regularity in tournaments (with M. Herzog), Theory and Applications of Graphs (Proceedings of the International Conference at Kalamazoo, 1976), Springer-Verlag Lecture Notes in Mathematics 642 (1978), 442-453.

  25. Degree frequencies in digraphs and tournaments (with B. Alspach), J. Graph Theory 2 (1978), 241-249.

  26. Score sets for tournaments, Congressus Numerantium 21, Utilitas Mathematica, Winnipeg (1978), 607-618.

  27. Tournaments (with L. W. Beineke), Chapter 7 in Selected Topics in Graph Theory (edited by L. W. Beineke and R. J. Wilson), Academic Press, London (1979), 169-204.

  28. Tournaments with prescribed numbers of kings and serfs, Congressus Numerantium 29, Utilitas Mathematica, Winnipeg (1980), 809-826.

  29. Every vertex a king. Discrete Math. 38 (1982), 93-98.

  30. Remarks on cohesion and induced edge connectivity.  Congressus Numerantium 38, Utilitas Mathematica, Winnipeg (1983), 253-260.

  31. Embedding oriented n-trees in tournaments (with N. C. Wormald), Studia Scientiarum Math. Hungarica 18 (1983), 377-387.

  32. Monochromatic reachability, complementary cycles and single arc reversals in tournaments, Graph Theory, Singapore 1983, (Proceedings of the First Southeast Asian Graph Theory Colloquium held in Singapore, May 1983), Springer-Verlag Lecture Notes in Mathematics 1073 (1984), 11-21.

  33. Stability of kings in tournaments (with M. F. Bridgland), Progress in Graph Theory (Proceedings of the 1982 Univ. of Waterloo Silver Jubilee Conference on Combinatorics) ed. by J. A. Bondy and U.S.R. Murty, Academic Press, 1984, 117-128.

  34. Two complementary cycles in two-connected tournaments, Annals of Discrete Mathematics 27 (1985), 321-334.

  35. Largest convex k-gons in convex n-gons (with C. Cordes), Discrete Applied Mathematics 14 (1986), 255-262.

  36. Minimum path decompositions of oriented cubic graphs (with K. Wayland), Journal of Graph Theory 11 (1987), 113-118.

  37. Bipartite graphs obtained from adjacency matrices of orientations of graphs, Discrete Mathematics 72 (1988), 321-330.

  38. Finding centers of certain tree-like networks (with Weizhen Gu), Congressus Numerantium 67 (1988), 265-278.

  39. Three problems on tournaments, Graph Theory and Its Applications:  East and West, Annals of the N. Y. Academy of Sciences 576 (1989), 466-473.

  40. Peripheral and eccentric vertices in products of graphs (with Weizhen Gu),   Congressus Numerantium 79 (1990), 79-88.

  41. Centroids to centers in trees, NETWORKS 21 (1991), 11-17.

  42. Majority tournaments: Sincere and sophisticated voting decisions under amendment procedure, Mathematical Social Sciences  21 (1991),  1-19.

  43. The relationship between two algorithms for decisions via sophisticated majority voting with an agenda,  Discrete Applied Mathematics  31 (1991), 23-28.

  44. Peripheral and eccentric vertices in graphs (with Weizhen Ghu), Graphs and Combinatorics 8 (1992), 361-375.

  45. Plurality preference digraph realized by trees, II: On realization numbers (with Weizhen Gu), Discrete Mathematics 101 (1992), 231-249.  Reprinted in The Julius Petersen Graph Theory Centennial (edited by L. Dovling Anderson, et. al.), Topics in Discrete Mathematics, Volume 6, Elsevier (1992).       

  46. Independent edges in bipartite graphs obtained from orientations of graphs (with John Gimble), Journal of Graph Theory 18 (1994), 515-533.

  47. Realization of digraphs by preferences based on distances in graphs (with Weizhen Gu and Walter Schnyder) , Journal of Graph Theory 19 (1995), 367-373.

  48.  Plurality preference digraphs realized by trees - I.  Necessary and sufficient conditions (with Weizhen Gu), Discrete Mathematics  147  (1995), 185-196.

  49.  Domination graphs of tournaments and digraphs (with David C. Fisher, J. Richard Lundgren, and Sarah Merz),  Congressus Numerantium 108 (1995), 97-107.

  50.  Tournaments: scores, kings, generalizations and special topics. (Invited survey) Surveys in Graph Theory (eds. G. Chartrand and M. Jacobson) Congressus Numerantium 115 (1996), 171-211.

  51.  Equitable agendas: agendas ensuring identical sincere and sophisticated voting decisions,  Social Choice and Welfare 14 (1997), 363-378.

  52. The k-ball l-path branch-weight centroid, Discrete Applied Mathematics (80) 2-3 (1997),  239-246.

  53.  Central k-trees of trees (with Fred McMorris), Congressus Numerantium 124 (1997), 139-144.

  54.  The domination and competition graphs of a tournament (with David C. Fisher, J.  Richard Lundgren, and Sarah Merz), J. Graph Theory 29 (1998), 103-110.

  55.  Score sequences for semicomplete digraphs (with C. Q. Zhang), Bulletin of the Institute of Combinatorics and its Applications 24 (1998), 27-32.

  56.  Balance vertices in trees, NETWORKS 34 (1999), 264-271.

  57.  Landau’s Theorem revisited (with Jerrold Griggs), The Australasian Journal of Combinatorics 20 (1999), 19-24.

  58. Domination graphs with nontrivial components, I (with David C. Fisher, David Guichard, J.       Richard Lundgren, and         Sarah Merz), Graphs and Combinatorics 17 (2001), no. 2, 227-236.

  59. Connected domination graphs of tournaments (with David C. Fisher,  J.  Richard Lundgren, and Sarah Merz), J. of         Combinatorial Mathematics and Combinatorial Computing 31 (1999), 169-176.

  60. The domination and competition graphs of tournaments (with David C. Fisher, J.  Richard Lundgren, and Sarah         Merz), Lie Algebras and Combinatorics, Proc. S. Korean Workshop on Algebra and Combinatorics 16, Part 1 (1997), 27-38.  [This is a summary of results in several other papers by the authors.]  

  61. Domination graphs with nontrivial components, II (with David C. Fisher, David Guichard, J. Richard Lundgren, and Sarah Merz), (accepted) to appear in The Bulletin of the Institute of Combinatorics and its Applications, 2001.

  62. Domination graphs with isolated components (with David C. Fisher, David Guichard, J Richard Lundgren, and Sarah Merz), (accepted) to appear in Ars Combinatoria.

  63. Total relative displacement of vertices in complete multipartite graphs, (accepted) to appear in the J. Graph Theory, 2002.

  64. Monotone reachability in arc-colored tournaments, Congressus Numerantium 146 (2000), 131-141.

  65. The latency center of a tree, submitted.

  66. Balance in trees (with Eli DePalma), submitted

  67.  Probalistic monotone reachability in arc-colored tournaments (with Tom Lewis), in preparation.

  68. Tournaments,  an invited chapter in a book on graph theory, Edited by G. Gross and J. Yellan, in preparation.

  69. Domination and irredundance parameters in tournaments (with Steven and Sandra Hedetniem and Alice McRae),
    draft in revision.

  70. Irredundance in tournaments (with Ed Palmer and Steve Hedetniemi), draft manuscript

  71. Eccentric digraphs of graphs (with diana Gu), draft manuscript.

  72. Tournament Ramsey theory (with B. Bollobás), rough draft.

In addition, I was co-editor for 29 volumes of Congressus Numerantium, a conference journal on numerical and combinatorial themes (ISSN 0384-9864), Vols. 1, 3, 17, 19, 32, 33, 35, 36, 39, 40, 43, 44, 45, 47, 48, 49, 53, 54, 55, 58, 59, 60, 65, 66, 67,76,77,78,79  (1970 - 1990).

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