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Publications, Mark Watkins

EX denotes "expository"; NR denotes "not refereed"

Accepted for publication

  1. Infinite graphs and planar maps, in: Topics in Graph Theory (R. Wilson and L. Beineke, eds.), CUPM series, Cambridge University Press, 20 pp. in January 2002. EX
  2. Cayley Maps (with B. Richter, J. Sirán, R. Jajcay, and T.W. Tucker), 82 pp. Accepted by J. Combin. Theory. Ser. B, in February 2001.
  3. Covalence sequences of planar vertex-homogeneous maps (with Jana Siagiová), 24 typeset pages. Accepted by Discrete Math. in August, 2004.

In Print

  1. Concentric Bilinski diagrams (with Jennifer A. Bruce), Australasian J. Combin. 30 (2004), 161-174.
  2. A characterization of infinite planar primitive graphs (with J. E. Graver), J. Combin. Theory Ser. B 91 (2004), 87 - 104.
  3. Automorphisms, Section 6.1 in: Handbook of Graph Theory (J. L. Gross and J. Yellen, eds.), pp. 485 -504, CRC Press, 2003. EX
  4. Planar embeddings with infinite faces (with C. Paul Bonnington, J. Graph Theory 42 (2003), 257 – 274.
  5. Realizing finite edge-transitive, orientable maps (with J. Sirán and T.W.Tucker), J. Graph Theory 37 (2001), 1-34. MR 2002b:05073
  6. Geodetic rays and fibers in periodic graphs (with P. Niemeyer), J. Graph Theory 34 (2000), 67 – 88. MR 2001b:05109
  7. Ends and automorphisms of infinite graphs, in Graph Symmetry: Algebraic Methods and Applications, (G. Hahn and G. Sabidussi, Eds.), pp.379 -414, NATO ASI Ser.C 497, Kluwer Academic Publishers, Dordrecht, 1997. MR 99b:05077 EX
  8. Geodetic rays and fibers in one-ended planar graphs (with P. Niemeyer), J. Combin. Theory, Ser. B 69 (1997), 142-163. MR 98d:05085
  9. MONOGRAPH. Locally Finite, Planar Edge-transitive Graphs (with J.E. Graver), Memoirs of the Amer. Math. Soc. Vol.126, No. 601, 1997, 75 pages. MR 97i:05001
  10. Separating double rays in locally finite, planar graphs (with C.P. Bonnington and W.Imrich), Discrete Math.145 (1995), 61-72. MR 97a:05070
  11. On translations of double rays in graphs, (with N. Polat), Per. Math. Hung. 30 (1995), 145-154. MR 96a:05074
  12. Sur les graphes infinis possédant un groupe d’automorphismes primitif, Discrete. Math. 130 (1994), 177-182. MR 95g:05090 EX
  13. Finite separating sets in locally finite graphs (with H.A. Jung), J. Combin. Theory (Ser. B) 59 (1993) 15-25. MR 94i:05053
  14. Some conditions for 1-transitivity, Discrete Math. 109 (1992) 289-296. MR 93j:05080
  15. Edge-transitive strips, Discrete Math. 95 (1991) 359-372. MR 93a:05068
  16. Vertex-transitive graphs that are not Cayley graphs, in: Cycles and Rays (G. Hahn, R.E. Woodrow, Ed.) NATO ASI Ser. C, Kluwer Academic Publishers, Dordrecht 1990, pp. 243-256. MR 91m:05099
  17. On bounded automorphisms of infinite graphs (with C. D. Godsil, W. Imrich, N. Seifter, and W. Woess), Graphs and Combin. 5 (1989), 333-338. MR 91c:05092
  18. The connectivities of locally finite primitive graphs (with H. A. Jung), Combinatorica 19 (1989), 261-267. MR 90k:05079
  19. Infinite vertex-transitive, edge-transitive, non-1-transitive graphs (with Carsten Thomassen), Proc. Amer. Math. Soc. 105 (1989), 258-261. MR 90a:05097
  20. A Characterization of finite planar primitive graphs (with J.E. Graver), Scientia 1 (1988), 59-60.
  21. Counterexamples to two conjectures about distance sequences (with J. B. Shearer). Discrete Math. 66 (1987), 289-298. MR 88k:05166
  22. Infinite paths that contain only shortest paths, J.Combin. Theory, Ser. B, 41 (1986), 341-355. MR 87m:05118.
  23. Computing the connectivities of circulant graphs,. Congressus Numerantium 49 (1985), 247-258. MR 87j:05107
  24. Fragments and automorphisms of infinite graphs (with H.A.Jung), Europ. J. Combinatorics, 5 (1984), 149-162. MR 86a:05062
  25. On infinite tournaments with regular automorphism groups (with D.A. Holton), Aequat. Math. 22 (1981), 46-53. MR 82k:05060
  26. Connectivity of infinite graphs having a transitive torsion group action (with L. Babai), Arch. Math. 34 (1980), 90-96. MR 81f:05091
  27. Les graphes de Cayley de connectivité un, in: Problèmes Combinatoires et Théorie des Graphes, Proc. of International Colloquium on Graph Theory, Orsay, France, July 1976, CNRS, Paris. 1978, pp. 419-422. MR 81a:05067
  28. BOOK. Combinatorics with Emphasis on the Theory of Graphs (with Jack E. Graver), Graduate Texts in Mathematics No.54, Springer-Verlag New York Inc., New York, 1977, 351 pages. MR 58 #21632. [Reviewed by Bull. Amer. Math. Soc. 1 (1979), 380-388.]
  29. On the Cayley index of a group, in: Proceedings of the International Conference on NR Combinatorial Theory, Canberra, Australia, August 16-27, 1977, (D. A. Holton, J. Seberry, Eds.), pp. 101-105, Springer-Verlag, Berlin, 1978. (Invited paper) MR 80m: 20036 EX NR
  30. Some remarks on transitive realizations of graphs, (with P. Hell and H. Levinson), Proc. of the Second Caribbean Conference on Combinatorics and Computing, Univ. of the West Indies (Cave Hill, Barbados), Jan. 4-7, 1977, (R.C. Read and C.C. Cadogan, Editors), pp. 115-122.
  31. On the structure of infinite vertex-transitive graphs (with H.A. Jung), Discrete Math. 18 (1977), 45-53. MR 58 #10578
  32. On the connectivities of finite and infinite graphs (with H.A. Jung), Monatsh. Math. 83 (1977), 121-131. MR 57 #159
  33. On automorphism groups of Cayley graphs (with W. Imrich), Per. Math. Hung. 7 (1976), 243-258. MR 56 #15483
  34. Infinite Caylety graphs of connectivity one, in: Proc. Second Combinatorial Conference, Western Michigan University, Kalamazoo, May 1976, Springer-Verlag, Berlin, 1978, pp. 599-607. (Invited paper) MR 58 #16388 EX
  35. Graphical regular representations of free products of groups, J. Combin. Theory (Ser. B), 21 (1976) 47-56. MR 54 #10068
  36. How small can the vertex-stabilizers of Cayley graphs be? in: Proceedings of the Conference on Algebraic Aspects of Combinatorics, (D. Corneil and E. Mendelsohn, editors) University of Toronto, 1975, pp. 79-87. (Invited paper) MR 52 #7963 EX NR
  37. The state of the GRR problem, in: Recent Advances in Graph Theory; Proc. Second Czechoslovak Conference on Graph Theory, (M. Fiedler, ed.) Prague, 1974, 517-522. (Invited paper) MR 52 #10488 EX NR
  38. Graphical regular representations of cyclic extensions of groups (with Wilfried Imrich). Pacific J. Math. 54 (1974) 1-17. MR 52 #174
  39. Graphical regular representations of alternating, symmetric, and miscellaneous small groups, Aequationes Math. 11 (1974), 40-50. MR 49 #8897
  40. Sur les groupes d’automorphismes de systèmes combinatoires, C.R. Acad. Sci. Paris 277 (1973) 831-833. MR 48 #3792
  41. On Graphical regular representations of C4 x Q, in: Graph Theory and Its Applications, Western Michigan Conference on Graph Theory and Its Applications. (Invited paper, May 1972). Springer-Verlag, Berlin, 1973, 305-311. MR 51 #253
  42. Graphical regular representations of direct products of groups (with L.A. Nowitz), Monatsh. Math. 76 (1972) 168-171. MR 46 #7801
  43. Graphical regular representations of non-abelian groups, I I (with L.A. Nowitz), Canad. J. Math., 24 (1972) 1009-1018. MR 47 #8345
  44. Graphical regular representations of non-abelian groups, I (with L.A. Nowitz), Canad. J. Math. 24 (1972), 993-1008. MR 47 #8345
  45. The groups of the generalized Petersen graphs, (with Roberto Frucht and Jack E. Graver), Proc. Cambridge Philos. Soc. 70 (1971), 211-219. MR 44 #6556
  46. On the action of non-abelian groups on graphs, J. Combin. Theory 11 (1971), 95-104. MR 43 #6136
  47. A special crossing number for bipartite graphs: a research problem, Annals of the New York Acad. Sci. 175 (1970), 405-410. MR 42 #120
  48. Still another product for graphs, in: Combinatorial Structures and Their Applications, Proceedings of the Calgary International Conference on Combinatorial Structures and their Applications, Calgary, Alberta, Canada, June 1969. Gordon and Breach, N.Y. 1970, 467-468.
  49. Connectivity of transitve graphs, J. Combin. Theory 8 (1970) 23-29. MR 42 #1707
  50. Some classes of hypoconnected vertex-transitive graphs, in: Recent Progress in Combinatorics; Proceedings of the Third Waterloo Combinatorial Conference, May 1968, W.T. Tutte, C. St.-J. A. Nash-Williams editors; Academic Press, New York,1969, 323-328. MR 41 #3316
  51. Above in abridged form in: Proof Techniques in Graph Theory, Proceedings of the Second Ann Arbor Graph Theory Conference, February, 1968, F. Harary, editor, Academic Press, New York, 1969, 171-177. EX NR
  52. A theorem on Tait colorings with an application to the generalized Petersen graphs, J. Combin. Theory, 6 (1969), 152-164. MR 38 #4360
  53. On the existence of certain disjoint arcs in graphs, Duke Math. J. 35 (1968), 231-246. MR 36 #6316
  54. On planar geodetic graphs, (with Joel G. Stemple) J. Combin. Theory, 4 (1968), 101-117. MR 36 #1354
  55. Cycles and connectivity in graphs (with D.M. Mesner), Canad. J. Math. 19 (1967), 319-328. MR 36 #1355
  56. A lower bound for the number of vertices of a graph, Amer. Math. Monthly, 74 (1967), 297. MR 34 #7407
  57. Characterization of planar geodetic graphs, J. Combin. Theory 2 (1967), 102-103. MR 34 #4166. EX
  58. Some theorems about n-vertex connected graphs (with D.M. Mesner), J. Math. Mech. 16 (1966), 321-326. MR 34 #94
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