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DOUGLAS BAUER Professor Mathematical Sciences Department Stevens Institute of Technology EDUCATION Ph.D., Stevens Institute of Technology, 1978 M.S., Stevens Institute of Technology, 1972 B.S., City College of New York, 1969 RESEARCH INTERESTS Graph theory; in particular problems in hamiltonian cycle theory, matching theory, extremal graph theory and graph connectivity. Network analysis; in particular the synthesis of reliable probabilistic networks. EXPERIENCE Professor of Mathematics, Stevens Institute of Technology (1990 - present) Associate Professor of Mathematics, Stevens Institute of Technology (1984 - 1990) Assistant Professor of Mathematics, Stevens Institute of Technology (1980 - 1984) Assistant Professor of Mathematics, Hofstra University (1979 - 1980) Instructor of Mathematics, Stevens Institute of Technology (1978 - 1979) Stevens Fellow (1977 - 1978) Teaching Assistant (1976 - 1977) Member of Technical Staff at Bell Laboratories, (1969 - 1976) VISITING POSITIONS Visiting Professor, Universitá di Roma, (November 2005) Visiting Professor, Universitá di Roma, (May 2004) Visiting Professor, Universitá di Roma, (May 2002) Visiting Professor, Universitá di Roma, (May 2001) Visiting Professor, Universitá di Roma, (June 1999) Visiting Professor, Universitá di Roma, (January 1997) Visiting Professor, Universitá di Roma, (May 1994) Research Fellow, Universiteit Twente, (Spring 1987) Visiting Professor, Universitá di Roma, (Fall 1986) PROFESSIONAL MEMBERSHIPS American Mathematical Society Mathematical Association of America Foundation Fellow of the Institute of Combinatorics and its Applications GRANTS 1. “A proposal in hamiltonian cycle theory”, funded by the National Security Agency in 1989 for 3 years. 2. “Long cycles in graphs” - Project Coordinator, funded by the NATO Collaborative Research Grants Programme. This is for work with Dr. H. J. Veldman, University of Twente, The Netherlands (1992-1997). 3. “Toughness and cycle structure” - Project Coordinator, funded by the NATO Collaborative Research Grants Programme. This is currently for work with Dr. H. J. Broersma, University of Twente, The Netherlands (1998-2001). PUBLICATIONS 1. D. Bauer and E. Schmeichel, Binding Number, Minimum Degree, and Cycle Structure in Graphs, submitted. 2. D. Bauer, H. Broersma, N. Kahl, E. Schmeichel, and J. van den Heuvel. Toughness and Vertex Degrees, submitted. 3. D. Bauer, N. Kahl, E. Schmeichel, and M. Yatauro. Best Monotone Degree Conditions for Binding Number, to appear in Discrete Mathematics. 4. D. Bauer, H. Broersma, N. Kahl, E. Schmeichel, and J. van den Heuvel. Degree sequences and the existence of k-factors, to appear in Graphs and Combinatorics. 5. D. Bauer, S. L. Hakimi, N. Kahl, and E. Schmeichel. Sufficient Degree Conditions for k-Edge-Connectedness of a Graph, NETWORKS, 54 (2009), 95 - 98. 6. D. Bauer, S. L. Hakimi, N. Kahl, and E. Schmeichel, The Strongest Monotone Lower Bound for the Independence Number of a Graph, Congressus Numerantium 192 (2008), 75 - 83. 7. D. Bauer, N. Kahl, L. McGuire, and E. Schmeichel, Long Cycles in Two-Connected Triangle-Free Graphs, Ars Combinatoria, 86 (2008) 295 - 304. 8. D. Bauer, H. J. Broersma, A. Morgana and E. Schmeichel, Tutte sets in graphs I: Maximal Tutte sets and D-graphs, J. Graph Theory, 55 (2007) 343 - 358. 9. D. Bauer, E. Schmeichel, and T. Surowiec, Subdivision of Edges and Matching Size, Ars Combinatoria, 84 (2007) 141 - 153. 10. D. Bauer, H. J. Broersma, N. Kahl, A. Morgana, E. Schmeichel and T. Surowiec, Tutte sets in graphs II: The complexity of finding Maximum Tutte sets, Discrete Applied Math.., 155 (2007) 1336 - 1343. 11. D. Bauer, H. J. Broersma and E. Schmeichel, Toughness in Graphs A Survey, Graphs and Combin., 22 no. 1, (2006) 1 - 35 12. D. Bauer, T. Niessen and E. Schmeichel, Toughness, Minimum Degree, and Spanning Cubic Subgraphs, J. Graph Theory, 45 (2004) 119 141 (Erratum J. Graph Theory, 46 (2004) 144). 13. D. Bauer, H. J. Broersma and E. Schmeichel, More Progress on Tough Graphs - The Y2K Report. The Proceedings of the Ninth Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms, and Applications, Electronic Notes in Discrete Math. 11 (July 2002) http://www.elsevier.nl/gej-ng/31/29/24/show/Products/notes/index.htt 14. D. Bauer, H. J. Broersma, A. Morgana and E. Schmeichel, Polynomial algorithms that prove an NP-hard hypothesis implies an NP-hard conclusion, Discrete Appl. Math., 120 (2002) 13 - 23. 15. D Bauer, L. McGuire, H. Trommel and H. J. Veldman, Long cycles in 3-cyclable graphs, Discrete Math 218 (2000) 1-8. 16. D. Bauer, H. J. Broersma and H. J. Veldman, Not every 2-tough graph is hamiltonian, Discrete Appl. Math., 99 (2000) 317 - 321. 17. D. Bauer, G. Y. Katona, D. Kratsch and H. J. Veldman, Chordality and 2-factors in tough graphs, Discrete Appl. Math., 99 (2000) 323 329. 18. D. Bauer, E. Schmeichel and H. J. Veldman, Progress on tough graphs - Another Four Years. In Y. Alavi, D. R. Lick and A. Schwenk, editors, Combinatorics, Graph Theory and Algorithms: Proceedings of the Eighth Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms, and Applications, Volume I, New Issues Press (1999) 69 - 88. 19. D Bauer, J. van den Heuvel, A. Morgana and E. Schmeichel, The complexity of toughness in regular graphs, Congr. Numer., 130 (1998) 47-61. 20. D. Bauer, J. van den Heuvel, A. Morgana and E. Schmeichel, The complexity of recognizing tough cubic graphs, Discrete Appl. Math., 79 (1997) 35 - 44. 21. D. Bauer, E. Schmeichel and H. J. Veldman, A note on dominating cycles in 2-connected graphs, Discrete Math 155 (1996) 13-18. 22. D. Bauer, J. van den Heuvel and E. Schmeichel, 2-Factors in trianglefree graphs, J. Graph Theory, 21 (1996) 405 - 412. 23. D. Bauer, J. van den Heuvel and E. Schmeichel, Toughness and trianglefree graphs, J. Combinat. Theory - Ser.B, 65 no 2 (1995) 208 - 221. 24. D. Bauer, H.J. Broersma and H.J. Veldman, On generalizing a theorem of Jung, Ars Combinatoria 40 (1995) 207 - 218. 25. D. Bauer, H. J. Broersma, J. van den Heuvel and H. J. Veldman, Long cycles in graphs with prescribed toughness and minimum degree, Discrete Math, 141 (1995) 1-10. 26. D. Bauer, E. Schmeichel and H. J. Veldman, Cycles in tough graphs - Updating the last four years. In Y. Alavi and A. Schwenk, editors, Graph Theory, Combinatorics , and Applications: Proceedings of the Seventh Quadrennial International Conference on the Theory and Applications of Graphs, Volume I , John Wiley and Sons (1995) 19-34. 27. D. Bauer, T. Niessen and E. Schmeichel, Neighborhood Unions, Degree Sums, Toughness, and 2-Factors, Congr. Numer., 100 (1994) 47-57. 28. D. Bauer, H. J. Broersma, J. van den Heuvel and H. J. Veldman, On Hamiltonian properties of 2-tough graphs, J. Graph Theory, 18 (1994) 539-543. 29. D. Bauer and E. Schmeichel, Toughness, minimum degree and the existence of 2-factors, J. Graph Theory, 18 (1994) 241 - 256. 30. D. Bauer, A. Morgana and E. Schmeichel, On the complexity of recognizing tough graphs, Discrete Math., 124 (1994) 13 - 17. 31. D. Bauer and E. Schmeichel, Toughness and the cycle structure of graphs, Ann. Discrete Math., 55 (1993) 145 - 152. 32. D. Bauer, G. Chen and L. Lasser, A degree condition for hamiltonian cycles in t-tough graphs with t > 1. In V.R. Kulli, editor, Advances in Graph Theory, Vishwa International Publications (1991) 20 - 33. 33. D. Bauer and E. Schmeichel, On a theorem of Häggkvist and Nicoghossian. In Y. Alavi, F.R.K. Chung, R.L. Graham and D. S. Hsu, editors, Graph Theory, Combinatorics, Algorithms, and Applications (1991) 20 - 25. 34. D. Bauer, G. Fan and H.J. Veldman, Hamiltonian properties of graphs with large neighborhood unions, Discrete Math., 96 (1991) 33 - 49. 35. D. Bauer, H.A. Jung and E. Schmeichel, On 2-connected graphs with small circumference, J. Combin. Inform. System Sci.,15 (1990) 16-24. 36. D. Bauer, E. Schmeichel and H.J. Veldman, Some recent results on long cycles in tough graphs. In Y. Alavi, G Chartrand, O. R. Oellermann and A. J. Schwenk, editors, Graph Theory, Combinatorics, and Applications: Proceedings of the 6th International Conference on the Theory and Applications of Graphs, John Wiley and Sons (1991) 113 - 123. 37. D. Bauer, H.J. Broersma and H.J. Veldman, Around three lemmas in hamiltonian graph theory. In R. Bodendick, R. Henn, editors, Topics in Combinatorics and Graph Theory, Physica-Verlag Heidelberg (1990) 101 - 110. 38. D. Bauer, H.J. Broersma and H.J. Veldman, On smallest nonhamiltonian regular tough graphs, Congr. Numer. 70 (1990) 95 - 98. 39. D. Bauer, S.L. Hakimi and E. Schmeichel, Recognizing tough graphs is NP-hard, Discrete Appl. Math., 28 (1990) 191 - 195. 40. D. Bauer and E. Schmeichel, Hamiltonian degree conditions which imply a graph is pancyclic, J. Combinat. Theory - Ser.B, 48 no 1 (1990) 111 - 116. 41. D. Bauer, A. Morgana, E. Schmeichel and H.J. Veldman, Long cycles in graphs with large degree sums, Discrete Math., 79 (1989/90) 59 70. 42. D. Bauer, A. Morgana and E. Schmeichel, A simple proof of a theorem of Jung, Discrete Math., 79 (1989/90) 147 - 152. 43. D. Bauer, H.J. Broersma, Li Rao and H.J. Veldman, A generalization of a result of Häggkvist and Nicoghossian, J. Combinat. Theory Ser.B, 47 no. 2 (1989) 237 - 243. 44. D. Bauer, E. Schmeichel and H.J. Veldman, A generalization of a theorem of Bigalke and Jung, Ars Combinatoria 26 (1988) 53 - 58. 45. D. Bauer and E. Schmeichel, Sufficient conditions for a graph to be pancyclic, Congr. Numer. 64 (1988) 211 - 214. 46. D. Bauer, A report on some short proofs of an Ore type theorem, Congr. Numer. 64 (1988) 55 - 57. 47. D. Bauer and E. Schmeichel, A proof of an extension of Ore’s theorem, Ars Combinatoria 24B (1987) 93 - 99. 48. D. Bauer, F. Boesch, C. Suffel and R. Van Slyke, On the validity of a reduction of reliable network design to a graph extremal problem, IEEE Transactions on Circuits and Systems, Vol. Cas-34, no 12, (1987) 1579 - 1581. 49. D. Bauer, A note on degree conditions for hamiltonian cycles in line graphs, Congr. Numer. 49 (1985) 11 - 18. 50. D. Bauer, F. Boesch, C. Suffel and R. Tindell, Combinatorial optimization problems in the design of probabilistic networks. NETWORKS, 15 (1985) 257 - 271. 51. D. Bauer, Extremal non-bipartite regular graphs of girth 4, J. Combinat. Theory - Ser.B, 37 no 1 (1984) 64 - 69. 52. D. Bauer, G. Bloom and F. Boesch, Edge to point degree lists and extremal triangle-free point degree regular graphs. In J. Adrian Bondy and U. S. R. Murty, editors, Progress in Graph Theory (1984) 93 - 103. 53. D. Bauer, Regular Kn -free graphs, J. Combinat. Theory - Ser.B, 35 no 2 (1983) 193 - 200. 54. D. Bauer, F. Harary, F. Nieminen and C. Suffel, Domination alteration sets in graphs, Discrete Math., 47 (1983) 153 - 161. 55. D. Bauer and R. Tindell, The connectivities of the middle graph, J. Combin. Inform. System Sci., 7 (1982) 54 - 55. 56. D. Bauer and R. Tindell, Graphs isomorphic to subgraphs of their line graphs, Discrete Math., 41 (1982) 1 - 6. 57. D. Bauer and R. Tindell, The connectivities of line and total graphs, J. Graph Theory, 6 (1982) 197 - 203. 58. D. Bauer, F. Boesch, C. Suffel and R. Tindell, Connectivity extremal problems and the design of reliable probabilistic networks, In Gary Chartrand, et. al., The Theory of Applications of Graphs: Proceedings of the 4th International Conference on the Theory and Applications of Graphs, John Wiley and Sons (1981) 45 - 54. 59. D. Bauer, Line graphical degree sequences, J. Graph Theory, 4 (1980) 219 - 232. 60. D. Bauer and R. Tindell, Graphs with prescribed connectivity and line graph connectivity, J. Graph Theory, 3 (1979) 393 - 395. 61. D. Bauer, On regular line graphs, Topics in Graph Theory, Annals of the New York Academy of Sciences, 328 (1979) 30 - 31.