S.C. Locke Research Publications

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Journal Articles

  1. D. Gray, S.C. Locke. Split-S-Nim. Submitted to Congressus Numerantium, March 2019, 15pp. Abstract.
  2. S.J. Curran, S.C. Locke, R.M. Low. C4-face magic labelings on Klein bottle checkerboards. Submitted to Electronic Journal of Combinatorics, June 2020, 34pp. Abstract
    On arXiv.org as "Equatorially balanced C4-face-magic labelings on Klein bottle grid graphs".
  3. S.J. Curran, S.C. Locke. C4-face-magic labelings on even order projective grid graphs. To appear in PROMS (Proceedings in Mathematics and Statistics), (accepted March 2022) 25 pp. Abstract
  4. S.J. Curran, S.C. Locke, R.M. Low. A variant of Nim played on Boolean matrices. Integers 23 (2023), #G4, 25 pp. Abstract.
  5. S.J. Curran, D. Gray, S.C. Locke, R.M. Low. Pyramid Nim. Integers 22(2022), #G2. 15 pp. Abstract
  6. S.C. Locke, B. Handley. Amalgamation Nim. Integers 21(2021), #G2, 14pp. Abstract
  7. W.H. Chan, Ardak Kapbasov, Arman Kapbasov, S.C. Locke, R.M. Low. A codex of N- and P- positions in Harary's 'Caterpillar Game'. Integers 21(2021), #G1, 26pp. Abstract [MR4213864]
  8. S.J. Curran, S.C. Locke, R.M. Low. C4-face magic toroidal labelings on Cm×Cn. The Art of Discrete and Applied Mathematics 4(2021), #P1.04, 33pp., https://adam-journal.eu/index.php/ADAM/article/view/1368/1191, Abstract [MR4193373]
  9. D. Gray, S.C. Locke. A variant of Nim. Discrete Mathematics 341(2018), 2485-2489. Abstract. [MR3828758]
  10. W.H. Chan, S.C. Locke, R.M. Low, and O.L. Wong. A map of the P-positions in 'Nim With a Pass' played on heap sizes of at most four. Discrete Applied Mathematics 244(2018), 44-55. Abstract. [MR3802534]
  11. S.C. Locke and S. Perry. Labelled Path Systems. Congressus Numerantium 229(2017), 95-100. Abstract. [MR3752207]
  12. S.C. Locke. Sum-free graphs. Journal of Combinatorics 8(2017), 349-370. (Dedicated to Professor J.A. Bondy.) Abstract. [MR3610742]
  13. C. Gottipati and S.C. Locke. Cohesion and non-separating trees in connected graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 99(2016), 69-79. Abstract. MR3585733]
  14. C. Gottipati and S.C. Locke. Reduced path systems and super-edge-graceful trees. Congressus Numerantium 216 (2013), 39-52. [MR3220071] Abstract.
  15. S.C. Locke and Wandi Wei. Infinite families of super edge-graceful trees. Congressus Numerantium 195(2009), 125-145. [MR2584291] Abstract.
  16. R.E.L. Aldred, R.P Anstee, and S.C. Locke. Perfect matchings after vertex deletions. Discrete Mathematics 307(2007), 3048-3054. [MR#2008k:05159] Abstract.
  17. M. Abreu and S.C. Locke. k-path-connectivity and mk-generation: an Upper Bound on m. Graph Theory in Paris: Trends in Mathematics. Birkhäuser Verlag Basel/Switzerland (2007), 11-19. [MR#2007j:05125] Abstract.
  18. M. Abreu, D. Labbate, and S.C. Locke. 6-path-connectivity and 6-generation. Discrete Mathematics 301 (2005), 20-27. (Combinatorics 2002 conference). Abstract. [MR#2006f:05102]
  19. F. Hadlock, F. Hoffman, and S.C. Locke. Manhattan graphs. Congressus Numerantium 171(2004), 25-32. Synopsis. [MR2122094]
  20. M. Abreu and S.C. Locke. Non-separating n-vertex trees in (2n+2)-cohesive graphs of diameter at most 4. Congressus Numerantium 154(2002), 21-30. Abstract. [MR#2004e:05102]
  21. S.C. Locke and C. Teng. Odd sums of long cycles in 2-connected graphs. Congressus Numerantium 159(2002), 19-30. Abstract. [MR#2004e:05100]
  22. S.C. Locke and H.-J. Voss. A distance-degree condition and non-separating paths: Solution to Problem 10647 [MAA Monthly 105 (1998), proposed by S.C.L.]. Incorporated into solution presented in MAA Monthly 108 (2001), 470-472.
  23. S.C. Locke and Y. Kaneko.The minimum degree approach for Paul Seymour's distance 2 conjecture. Congressus Numerantium 148(2001), 201-206. [MR# 200k:05078]
  24. M. Barovich and S.C. Locke, The cycle space of a 3-connected hamiltonian graph. Discrete Mathematics 220(2000), 13-33. Abstract. [MR# 2001d:05099]
  25. S.C. Locke and D. Witte. On non-hamiltonian circulant digraphs of outdegree three. Journal of Graph Theory 30(1999), 319-331. Abstract. [MR# 99m:05069]
    Dave Witte, dwitte@math.okstate.edu, has stored preprints: LATEX 2e file (requires Journal of Graph Theory macros); or PostScript file.
  26. S.C. Locke. Further notes on: largest triangle-free subgraphs in powers of cycles. Ars Combinatoria 49(1998), 65-77. Abstract. dvi. [MR# 99c:05106]
  27. S.C. Locke and Feng Lou. Finding independent sets in K4-free 4-regular connected graphs. Journal of Combinatorial Theory, Series B 71 (1997), pages 85-110. Abstract. [MR# 98h:05104]
  28. K. Fraughnaugh and S.C. Locke. Lower bounds on size and independence in K4-free graphs. Journal of Graph Theory 26 (1997), pages 61-71. Abstract. [MR# 98h:05099]
  29. K. Fraughnaugh and S.C. Locke. Finding independent sets in triangle-free graphs. S.I.A.M. Journal of Discrete Mathematics 9(1996), 674-681. Abstract. [MR# 96f:05180]
  30. K. Fraughnaugh and S.C. Locke. 11/30 (finding large independent sets in connected triangle-free 3-regular graphs). Journal of Combinatorial Theory, Series B 65(1995), 51-72. K. Fraughnaugh: KFraughn@carbon.cudenver.edu. Abstract. [MR# 96f:05099]
  31. J.A. Bondy and S.C. Locke. Triangle-free subgraphs of powers of cycles. Graphs and Combinatorics 8(1992), 109-118. [MR# 93e:05079] Abstract.
  32. S.C. Locke. Long paths and the cycle space of a graph. Ars Combinatoria 33(1992), 77-85. [MR# 94d:05076] Abstract.
  33. S.C. Locke and C.-Q. Zhang. Cycles through three vertices in 2-connected graphs. Graphs and Combinatorics 7(1991), 265-269. [MR# 93a:05078] Abstract.
  34. F. Hoffman, A.D. Meyerowitz and S.C. Locke. A note on cycle double covers of Cayley graphs. Mathematica Pannonica 2(1991), 63-66. [MR# 92g:05145] Abstract.
  35. Y. Egawa, R. Glas and S.C. Locke. Cycles and paths through specified vertices in k-connected graphs. Journal of Combinatorial Theory, Series B, 52(1991), 20-29. [MR# 92i:05132] Abstract.
  36. B. Alspach, S.C. Locke and D. Witte. The Hamilton spaces of Cayley graphs on abelian groups. Discrete Mathematics 82(1990), 113-126. [MR# 91h:05058] Abstract.
  37. S.C. Locke. A note on bipartite subgraphs of triangle-free regular graphs. Journal of Graph Theory 14(1990), 181-185. [MR# 91b:05107] Abstract.
  38. S.C. Locke and D. Witte. Flows in circulant graphs of odd order are sums of Hamilton cycles. Discrete Mathematics 78(1989), 105-114. (Volume dedicated to Torrence Parsons.) [MR# 91e:05048] Abstract.
  39. M.O. Albertson, S.T. Hedetniemi, R.E. Jamison and S.C. Locke. The subchromatic number of a graph. Discrete Mathematics 74(1989), 33-49. [MR# 90f:05057] Abstract.
    Also: Book Chapter, 1989, Graph Coloring and Variations, pages 33-49.
  40. S.C. Locke. Extremal 3-connected graphs. Discrete Mathematics 68(1988), 257-263. [MR# 89:05109] Abstract.
  41. J.A. Bondy and S.C. Locke. Largest bipartite subgraphs in triangle-free graphs with maximum degree three. Journal of Graph Theory 10(1986), 477-504. [MR# 87m:05105] Abstract.
  42. S.C. Locke. Bipartite density and the independence ratio. Journal of Graph Theory 10(1986), 47-53. [MR# 87d:05079] Abstract.
  43. S.C. Locke. A basis for the cycle space of a 2-connected graph. European Journal of Combinatorics 6(1985), 253-256. [MR# 87g:05138] Abstract.
  44. S.C. Locke. A generalization of Dirac's theorem. Combinatorica 5(1985), 149-159. [MR# 87c:05077] Abstract.
  45. S.C. Locke. A basis for the cycle space of a 3-connected graph. Cycles in Graphs, North-Holland Mathematical Studies 115, Annals of Discrete Mathematics 27(1985), 381-397. [MR# 87h:05136] Abstract.
  46. S.C. Locke. Extremal Properties of Paths, Cycles and k-colourable Subgraphs of Graphs. Ph.D. Thesis, Department of Combinatorics and Optimization, University of Waterloo (1982). (Approximately 260 pages.) Abstract.
  47. S.C. Locke. Maximum k-colourable subgraphs. Journal of Graph Theory 6(1982), 123-132. [MR# 83i:05046] Abstract.
  48. S.C. Locke. Relative lengths of paths and cycles in k-connected graphs. Journal of Combinatorial Theory, Series B, 32(1982), 206-22. [MR# 83f:05036] Abstract.
  49. J.A. Bondy, I. Ben-Arroyo Hartman and S.C. Locke. A new proof of a theorem of Dirac. Proceedings of the Twelfth Southeastern Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium 32(1981), 131-136. [MR# 84c:05055] Abstract.
  50. J.A. Bondy and S.C. Locke. Relative lengths of paths and cycles in 3-connected graphs. Discrete Mathematics 33(1981), 111-122. [MR#82b:05088] Abstract.
  51. J.A. Bondy and S.C. Locke. Relative lengths of paths and cycles in k-connected graphs. Proceedings of the First Joint Canada-France Combinatorial Colloquium, Annals of Discrete Mathematics 8(1980), 253-259. [MR# 81k:05067] Abstract.

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Florida Atlantic University
777 Glades Road
Boca Raton, Florida 33431-0991

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Phone: (561) 297-3350.
Fax: (561) 297-2436.
URL: http://math.fau.edu/locke/research.htm

Last modified October 14, 2016, by S.C. Locke.