Dan Cranston's Papers

Papers

You can find reviews of many of these papers on MathSciNet (subscription required).
Most of my papers are also available on the arxiv.

H-index 14 and 742 citations in Google Scholar as of 08/12/2020.

Papers Submitted for Publication

58. Vertex Partitions into an Independent Set and a Forest with Each Component Small. Daniel W. Cranston and Matthew P. Yancey.
57. Coloring (P₅, gem)-free graphs with Δ - 1 colors. Daniel W. Cranston, Hudson Lafayette, and Landon Rabern.

Refereed Journal Publications

56. Sparse Graphs are Near-bipartite Daniel W. Cranston and Matthew P. Yancey. SIAM Journal on Discrete Math. To appear. pdf
55. Circular Flows in Planar Graphs. Daniel W. Cranston and Jiaao Li. SIAM Journal on Discrete Math. Vol. 34(1), 2020, pp. 497-519. pdf
54. Degeneracy and Colorings of Squares of Planar Graphs without 4-Cycles. Ilkyoo Choi, Daniel W. Cranston, and Théo Pierron. Combinatorica. To appear. pdf
53. A Note on Bootstrap Percolation Thresholds in Plane Tilings using Regular Polygons. Neal Bushaw and Daniel W. Cranston. Australasian J. Combinatorics. Vol. 74(3), 2019, pp. 486-497. pdf
52. The Hilton-Zhao Conjecture is True for Graphs with Maximum Degree 4. Daniel W. Cranston and Landon Rabern. SIAM Journal on Discrete Math. 33(3), 2019, pp. 1228-1241. (12pp) pdf
51. A Characterization of (4,2)-Choosable Graphs. Daniel W. Cranston. Journal of Graph Theory. To appear. pdf
50. Acyclic Edge-coloring of Planar Graphs: Δ Colors Suffice when Δ is Large. Daniel W. Cranston. SIAM Journal on Discrete Math. Vol. 33(2), 2019, pp. 614-628. (14pp) pdf
49. Proper Distinguishing Colorings with Few Colors for Graphs with Girth at Least 5 Daniel W. Cranston. Electronic Journal of Combinatorics. Vol. 25(3), 2018, #P3.5. (15pp) pdf
48. Planar Graphs of Girth at least Five are Square (Δ + 2)-Choosable. Marthe Bonamy, Daniel W. Cranston, and Luke Postle. Journal of Combinatorial Theory, Series B. Vol. 134, 2019, pp. 218-238. (18pp) pdf
47. Planar Graphs are 9/2-colorable. Daniel W. Cranston and Landon Rabern. Journal of Combinatorial Theory, Series B. Vol. 133, 2018, pp. 32-45. pdf slides
46. Beyond Degree Choosability. Daniel W. Cranston and Landon Rabern. Electronic Journal of Combinatorics. Vol. 24(3), 2017, #P3.29. (14pp) pdf
45. Short Fans and the 5/6 Bound for Line Graphs. Daniel W. Cranston and Landon Rabern. SIAM Journal on Discrete Math. Vol. 31(3), 2017, pp. 2039-2063. pdf
44. List-coloring Claw-free Graphs with Δ-1 colors. Daniel W. Cranston and Landon Rabern. SIAM Journal on Discrete Math. Vol. 31(2), 2017, pp. 726-748. (24pp) pdf
43. Edge Lower Bounds for List Critical Graphs, via Discharging. Daniel W. Cranston and Landon Rabern. Combinatorica. Vol. 38(5), October 2018, pp. 1045-1065. (17pp) pdf
42. Subcubic Edge Chromatic Critical Graphs have Many Edges. Daniel W. Cranston and Landon Rabern. Journal of Graph Theory. Vol. 86(1), September 2017, pp. 122-136. (15pp) pdf
41. An Introduction to the Discharging Method via Graph Coloring. Daniel W. Cranston and Douglas B. West. Discrete Math. Vol. 340, no. 4, April 2017, pp. 766-793. (50pp) pdf Extended version: A Guide to the Discharging Method. (77pp) pdf
40. Coloring Squares of Planar Graphs with no 4-cycles and no 5-cycles. Daniel W. Cranston and Robert Jaeger. Journal of Graph Theory. Vol. 85(4), August 2017, pp. 721-737. (15pp) pdf
39. Modified Linear Programming and Class 0 Bounds for Graph Pebbling. Daniel W. Cranston, Luke Postle, Chenxiao Xue, and Carl Yerger. J. Combinatorial Optimization. 34(1), July 2017, pp. 114-132. (19pp) pdf
38. Planar Graphs have Independence Ratio at least 3/13. Daniel W. Cranston and Landon Rabern. Electronic Journal of Combinatorics. Vol. 23(3), 2016, #P3.45. pdf
37. Painting Squares in Δ²-1 Shades. Daniel W. Cranston and Landon Rabern. Electronic Journal of Combinatorics. Vol. 23(2), 2016, #P2.50. pdf slides
36. Graphs with χ=Δ have Big Cliques. Daniel W. Cranston and Landon Rabern. SIAM Journal on Discrete Math. Vol. 29(4), 2015, pp. 1792-1814. (24pp) pdf slides
35. The Fractional Chromatic Number of the Plane. Daniel W. Cranston and Landon Rabern. Combinatorica. Vol. 37(5), October 2017, pp. 837-861. (20pp) pdf slides
34. A Note on Coloring Vertex-transitive Graphs. Daniel W. Cranston and Landon Rabern. Electronic Journal of Combinatorics. Vol. 22(2), 2015, #P2.1. (8pp) pdf
33. Brooks' Theorem and Beyond. Daniel W. Cranston and Landon Rabern. J. Graph Theory. Vol. 80(3), November 2015, pp. 199-225. (25pp) pdf
32. On the Boundedness of Positive Solutions of the Reciprocal Max-Type Difference Equation x_n=max_1≤i≤t(Aⁱ_n-1/x_n-i) with Periodic Parameters. Daniel W. Cranston and Candace M. Kent. Applied Mathematics and Computations. Vol. 221 (2013) pp. 144-151. pdf slides
31. The 1, 2, 3-Conjecture and 1, 2-Conjecture for Sparse Graphs. Daniel W. Cranston, Sogol Jahanbekam, and Douglas B. West. Discussiones Mathematicae Graph Theory. Vol. 34(4), 2014, pp. 769–799. (29pp) pdf
30. Regular graphs of odd degree are antimagic. Daniel W. Cranston, Yu-Chang Liang, and Xuding Zhu. Journal of Graph Theory. Vol. 80(1), September 2015, pp. 28--33. (5pp) pdf
29. Sufficient sparseness conditions for G² to be (Δ+1)-choosable, when Δ ≥ 5. Daniel W. Cranston and Riste Skrekovski. Discrete Applied Math. Vol. 162(10), January 2014, pp. 167-176. pdf
28. Choosability of the square of a planar graph with maximum degree four. Daniel W. Cranston, Rok Erman, and Riste Skrekovski. Australasian Journal of Combinatorics. Vol 59(1), June 2014, pp. 86-97. pdf
27. Game matching number of graphs. Daniel W. Cranston, William B. Kinnersley, Suil O, and Douglas B. West. Discrete Applied Math. Vol. 161(13-14), 2013, pp. 1828-2836. pdf
26. Coloring claw-free graphs with Δ-1 colors. Daniel W. Cranston and Landon Rabern. SIAM J. Discrete Math. 27(1) (2013), 534-549. pdf slides
25. Hamiltonicity in Connected Regular Graphs. Daniel W. Cranston and Suil O. Information Processing Letters Vol. 113, 2013, pp. 858-860. (5pp) pdf
24. Conjectures equivalent to the Borodin-Kostochka conjecture that a priori seem weaker. Daniel W. Cranston and Landon Rabern. Submitted. (45pp) pdf slides
23. Revolutionaries and Spies: Spy-good and Spy-bad graphs. Jane V. Butterfield, Daniel W. Cranston, Gregory J. Puleo, Douglas B. West, and Reza Zamani. Theoretical Computer Science. Vol. 463 (2012), pp. 35-53. pdf slides
22. Revolutionaries and Spies on Trees and Unicyclic Graphs. Daniel W. Cranston, Clifford Smyth, and Douglas B. West. Journal of Combinatorics. Vol. 3(2) pp. 195-206. pdf slides
21. New Results in t-tone Coloring of Graphs. Daniel W. Cranston, Jaehoon Kim, and William B. Kinnersley. Electronic Journal of Combinatorics. Vol. 20, (2013) #P17. (13pp) pdf E-JC
20. Chain-making Games in Grid-like Posets. Daniel W. Cranston, Bill Kinnersley, Kevin Milans, Greg Puleo, and Douglas B. West. Journal of Combinatorics. Vol. 3(4) pp. 633-650. pdf slides
19. List Colorings of K₅-minor-free Graphs with Special List Assignments. Daniel W. Cranston, Anja Pruchnewski, Zsolt Tuza, Margit Voigt. Journal of Graph Theory. Vol. 71(1), September 2012, pp. 18--30. pdf slides
18. Linear Choosability of Sparse Graphs. Daniel W. Cranston and Gexin Yu. Discrete Math. Vol. 311, no. 17, 6 September 2011, pp. 1910-1917. pdf slides
17. Overlap Number of Graphs. Daniel W. Cranston, Nitish Korula, Tim LeSaulnier, Kevin Milans, Chris Stocker, Jennifer Vandenbussche, and Douglas B. West. Journal of Graph Theory. Vol. 70(1), May 2012, pp. 10-28. pdf slides
16. Injective Colorings of Graphs with Low Average Degree. Daniel W. Cranston, Seog-Jin Kim, and Gexin Yu. Algorithmica. Vol. 60(3), July 2011, pp. 553-568. pdf
15. Injective Colorings of Sparse Graphs. Daniel W. Cranston, Seog-Jin Kim, and Gexin Yu. Discrete Math. Vol. 310, no. 21, 6 November 2010, pp. 2965-2973. pdf slides
14. A New Lower Bound on the Density of Vertex Identifying Codes for the Infinite Hexagonal Grid. Daniel W. Cranston and Gexin Yu. Electronic Journal of Combinatorics. Vol. 16, (2009) #R113. (15pp) pdf slides E-JC
13. Crossings, Colorings, and Cliques. Michael O. Albertson, Daniel W. Cranston, and Jacob Fox. Electronic Journal of Combinatorics. Vol. 16, (2009) #R45. (11pp) pdf slides E-JC
12. (7,2)-edge-choosability of 3-regular graphs. Daniel W. Cranston and Douglas B. West. SIAM Journal of Discrete Math. Vol. 23(2), April 2009, pp. 872-881. pdf
11. Star Coloring of Sparse Graphs. Yuehua Bu, Daniel W. Cranston, Mickael Montassier, Andre Raspaud, and Weifan Wang. Journal of Graph Theory. Vol. 62(3), November 2009, pp. 201-219. pdf slides
10. Mulitgraphs with Δ ≥ 3 are Totally-(2Δ-1)-Choosable. Daniel W. Cranston. Graphs and Combinatorics. Vol. 25(1), May 2009, pp. 35-40. pdf
9. Edge-choosability and Total-choosability of Planar Graphs with no Adjacent 3-cycles. Daniel W. Cranston. Discussiones Mathematicae Graph Theory. Vol. 29 (1), pp. 163-178. pdf slides
8. Research at ASMSA Based on the DIMACS Biomath Program. Charles Mullins and Daniel W. Cranston. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. (6pp) pdf
7. Regular Bipartite Graphs are Antimagic. Daniel W. Cranston. Journal of Graph Theory. Vol. 60, March 2009, pp. 173-182. pdf slides
6. Choice number of complete multipartite graphs K_{3*3,2*(k-5),1*2} and K_{4,3*2,2*(k-6),1*3}. Wenjie He, Lingmin Zhang, Daniel W. Cranston, Yufa Shen, and Guoping Zheng. Discrete Math. Vol 308, no. 23, 6 December 2008, pp. 5871-5877. pdf
5. Nomadic Decompositions of Bidirected Complete Graphs. Daniel W. Cranston. Discrete Math. Vol. 308, no. 17, 6 September 2008, pp. 3982-3985. pdf
4. Pebbling and Optimal Pebbling in Graphs. David Bunde, Erin Chambers, Daniel W. Cranston, Kevin Milans, and Douglas West. Journal of Graph Theory. Vol. 57, March 2008, pp. 215-238. pdf
3. List-coloring the Square of a Subcubic Graph. Daniel W. Cranston and Seog-Jin Kim. Journal of Graph Theory. Vol. 57, January 2008, pp. 65-87. pdf slides more slides
2. Short Proofs for Cut-and-Paste Sorting of Permutations. Daniel W. Cranston, Hal Sudborough, and Douglas West. Discrete Math. Vol. 307, no. 22, 28 October 2007, pp. 2866-2870. pdf slides
1. Strong Edge-Coloring of Graphs with Maximum Degree 4 using 22 Colors. Daniel W. Cranston. Discrete Math. Vol. 306, no. 21, 6 November 2006, pp. 2772-2778. pdf
0. Coloring and Labeling Problems in Graphs. Daniel W. Cranston. Doctoral Thesis, May 2007. pdf

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