[5] M. Budden, A. Collins*, K. Ellis Lea*, and S. Savioli*,
Rational Residuacity of Primes, Involve 3 (2010), 249-257.
pdf (Note that
F. Lemmermeyer has pointed out a mistake in the proof of Theorem 2.)
[6] B. Budden, M. Budden, G. Case, and M. Cherry,
Characteristic Count Rate Profiles for a Rotating Modulator Gamma-Ray Imager, Astrophysics and Space Science 334 No. 1 (2011), 61-69.
pdf
[7] M. Budden, N. Calkins*, W. Hack*, J. Lambert, and K. Thompson*,
Enumeration of Triangles in Quartic Residue Graphs, Integers 11 (2011), #A48 (16 pages) (electronic);
Integers 12 (2012) 57-73 (print).
pdf
[8] M. Budden, S. Eastman, S. King*, and A. Moisant*,
Permutations of Rational Residues, Acta Universitatis Apulensis 28 (2011), 333-339.
pdf
[9] M. Budden, N. Calkins*, W. Hack*, J. Lambert, and K. Thompson*,
Dirichlet Character Difference Graphs, Acta Mathematica Universitatis Comenianae 82, No. 1 (2013), 21-28.
pdf
[10] R. Atanasov, M. Budden, J. Lambert, K. Murphy*, and A. Penland**,
On Certain Induced Subgraphs of Paley Graphs, Acta Universitatis Apulensis 40 (2014), 51-65.
pdf
[11] R. Atanasov, M. Budden, and J. Lambert,
Character Difference Digraphs over Finite Fields, Rendiconti del Seminario Matematico della Université di Padova 133 (2015), 103-115.
pdf
[12] M. Budden, J. Hiller**, and A. Rapp**,
Generalized Ramsey Theorems for r-Uniform Hypergraphs,
Australasian Journal of Combinatorics 63 (2015), 142-152.
pdf
[13] M. Budden and A. Rapp**,
Constructing r-Uniform Hypergraphs with Restricted Clique Numbers,
The North Carolina Journal of Mathematics and Statistics 1 (2015), 30-34.
pdf
[14] M. Budden, J. Hiller**, and A. Rapp**,
Hypergraph Ramsey Numbers Involving Paths, Acta Universitatis Apulensis 48 (2016), 75-87.
pdf
[15] M. Budden, J. Hiller**, J. Lambert, and C. Sanford*,
The Lifting of Graphs to 3-Uniform Hypergraphs and Some Applications to Hypergraph Ramsey Theory, Involve 10 (2017), 65-76.
pdf
[16] M. Budden and G. Goehle,
Local Coefficient Matrices and the Metaplectic Correspondence, Journal of Lie Theory 27 (2017), 657-670.
pdf
[17] M. Budden, M. Stender*, and Y. Zhang,
Weakened Ramsey Numbers and Their Hypergraph Analogues, Integers 17 (2017), #A23 (8 pages).
pdf
[18] M. Bruce*, M. Budden, and J. Hiller,
Lexicographic Products of r-Uniform Hypergraphs and Applications to Hypergraph Ramsey Theory,
Australasian Journal of Combinatorics 70 (2018), 390-401.
pdf
[19] G. Beam* and M. Budden,
Weakened Gallai-Ramsey Numbers, Surveys in Mathematics and its Applications 13 (2018), 131-145.
pdf
[20] M. Budden and A. Penland,
Trees and n-Good Hypergraphs, Australasian Journal of Combinatorics 72 (2018), 329-349.
pdf
[21] M. Budden and E. DeJonge*,
Destroying the Ramsey Property by the Removal of Edges, Australasian Journal of Combinatorics 74 (2019), 476-485.
pdf
[22] M. Budden and A. Penland,
Corrigendum: Trees and n-Good Hypergraphs, Australasian Journal of Combinatorics 75 (2019), 171-173.
pdf
[23] M. Budden, J. Hiller, and A. Penland,
Constructive Methods in Gallai-Ramsey Theory for Hypergraphs, Integers 20A (2020), #A4.
pdf
[24] M. Budden,
Schur Numbers Involving Rainbow Colorings, Ars Mathematica Contemporanea 18 (2020), 281-288.
pdf
[25] M. Budden and J. Clifton*,
A Weakened Version of Strict Schur Numbers, Acta Universitatis Apulensis 65 (2021), 111-122.
pdf
[26] M. Budden, J. Hiller, T. Meek*, and A. Penland,
Algebraic Properties of a Hypergraph Lifting Map, Integers 21 (2021), #A77 (12 pages).
pdf
[27] M. Budden and W. Stiles*,
Anti-Ramsey Hypergraph Numbers, Electronic Journal of Graph Theory and Applications 9 (2021), 397-407.
pdf
[28] M. Budden,
The Gallai-Ramsey Number for a Tree Versus Complete Graphs, Ron Graham Memorial Volume,
Integers 21A (2021), #A7 (6 pages) (electronic); In:
Number Theory and Combinatorics: A Collection in Honor of the Mathematics of Ronald Graham, De Gruyter Proc. Math., De Gruyter, Berlin, 2022, 109-113 (print).
pdf
[29] M. Budden, J. Hiller, and A. Penland,
Minimally Connected r-Uniform Hypergraphs, Australasian Journal of Combinatorics 82 (2022), 1-20.
pdf
[30] M. Budden and J. Hiller,
Sierpiński Products of r-Uniform Hypergraphs, The Art of Discrete and Applied Mathematics 5 (2022), #P1.06 (13 pages).
pdf
[31] M. Budden and B. Collins*,
Some Variations of Multicolor Rado Numbers,
Acta Universitatis Apulensis 69 (2022), 93-105.
pdf
[32] M. Budden and E. DeJonge*,
Multicolor Star-Critical Ramsey Numbers and Ramsey-Good Graphs, Electronic Journal of Graph Theory and Applications 10 (2022), 51-66.
pdf
[33] M. Budden and T. Wimbish*,
Subgraphs of Gallai-Colored Complete Graphs Spanned by Edges Using at Most Two Colors, Australasian Journal of Combinatorics 84 (2022), 375-387.
pdf
[34] M. Budden and J. Clifton*,
Hypergraph Ramsey Numbers Involving Trees, Stars, and Complete Hypergraphs, Integers 22 (2022), #A92 (14 pages).
pdf
[35] M. Budden and Z. Daouda*,
Star-Critical Gallai-Ramsey Numbers Involving the Disjoint Union of Triangles,
The Art of Discrete and Applied Mathematics 6 (2023), #P1.09 (9 pages).
pdf
[36] M. Budden,
Ramsey Numbers for Connected 2-Colorings of Complete Graphs, Theory and Applications of Graphs 10 (2023), Article 7 (10 pages).
pdf
[37] M. Budden,
The Multicolor Star-Critical Gallai-Ramsey Number for a Path of Order 5,
Discrete Mathematics Letters 12 (2023), 145-149.
pdf
[38] M. Budden and H. Privette*,
Multicolor Ramsey Theory for a Fan Versus Complete Graphs, Discrete Mathematics Letters 13 (2024), 143-149.
pdf
[39] M. Budden and B. Landman,
Rainbow Numbers for the Generalized Schur Equation x_1+x_2+...+ x_{m-1} = x_m, Australasian Journal of Combinatorics 90 (2024), 66-79.
pdf
[40] M. Moun**, J. Jakhar, and M. Budden,
Star-Critical Connected Ramsey Numbers for 2-Colorings of Complete Graphs, Transactions on Combinatorics 14 (2025), 211-222.
pdf
[41] M. Budden and T. Wimbish**,
Connected Ramsey Numbers Involving Trees, Electronic Journal of Mathematics 9 (2025), 31-37.
pdf
[42] J. Jakhar, M. Budden, and M. Moun**,
Rainbow Numbers in Planar Host Graphs, Filomat 39(8) (2025), 2695-2710.
pdf
[43] M. Budden and R. Prange*,
Ramsey Theory for a Generalized Fan Versus Triangles, Utilitas Mathematica 123 (2025), 165-178.
pdf
[44] M. Budden,
The Star-Critical Weakened Gallai-Ramsey Number gr^{2,t}_*(C_5), Filomat 39(24) (2025), 8545-8549.
pdf
[45] M. Budden, M. Moun**, and J. Jakhar,
Star-Critical Weakened Ramsey Numbers, Theory and Applications of Graphs 12(2) (2025), Article 4 (16 pages).
pdf
[46] M. Budden and R. Prange**,
The Star-Critical Gallai-Ramsey Number gr_*(F_{3,2},K_3,K_3) and Related Critical Colorings, Congressus Numerantium 236 (2025), 115-122.
pdf
[47] M. Budden, M. Moun**, and J. Jakhar,
The Multicolor Star-Critical Gallai-Ramsey Number for a Path of Order 6, The Art of Discrete and Applied Mathematics 9 (2026), #P1.05 (9 pages).
pdf
[48] M. Budden,
Weakened Gallai-Ramsey Numbers for Fans, Utilitas Mathematica 127 (2026), 65-73.
pdf
[49] M. Budden, L. Goch*, and J. Hiller,
Computational Lower Bounds for Weakened Ramsey Numbers from Strongly Regular t-Colorings of Complete Graphs,
Bulletin of the Institute of Combinatorics and its Applications 107 (2026), 56-67.
pdf
[50] M. Budden, M. Moun**, J. Jakhar, and R. Prange**,
Multicolor Connected Ramsey Numbers, Australasian Journal of Combinatorics 95(2) (2026), 364-380.
pdf
[51] M. Budden, Y.S. Khobragade**, and S. Sarkar,
Lower Bounds for Multicolor Star-Critical Ramsey Numbers, under review.
preprint
[52] Z. Wang, L. Zhang, M. Wei, and M. Budden,
Gallai-Ramsey Numbers for \ell-Connected Graphs, under review.
preprint
[53] M. Budden and A. Gregory,
Weakened Gallai-Ramsey Numbers for Books, under review.
preprint
Articles in Preparation (* indicates undergraduate student coauthor, ** indicates graduate student coauthor):
[54] M. Budden and E. DeJonge,
The 3-Color 2-Chromatic Gallai-Ramsey Number for Complete Graphs.
[55] M. Budden, J. Hiller, and H. Privette**,
The H-Join of Families of r-Uniform Hypergraphs.
[56] M. Budden, Y. Mao, R. Prange**, and M. Wei,
Gallai-Ramsey Theory for Multiple Triangles.
[57] J. Alm, M. Budden, and A. Gregory,
Star-Critical Ordered Ramsey Numbers.
[58] M. Moun and M. Budden
, Weakened Rainbow Numbers.
[59] M. Budden and P. Poudel*,
3-Color (1,2)-Chromatic Gallai-Ramsey Numbers Involving Stars.
[60] M. Budden, A. Gregory, and S. Sullivan*,
Variations on the Pebbling Number of a Graph.
Other Publications:
[1] B. Bailey, M. Budden, and U. Ghosh-Dastidar, Practical Tips for Managing Challenging Scenarios in Undergraduate Research, MAA Online Column: Resources for Undergraduate Research in Mathematics 3 (2008). pdf
[2] B. Bailey, M. Budden, M. Dorff, and U. Ghosh-Dastidar,
Undergraduate Research: How Do We Begin?, MAA Focus 29, No. 1 (2009), 14-16.
pdf
Conference Organization:
PANTS X (PAlmetto Number Theory Series) held at Armstrong Atlantic State University September 19-20, 2009.
SERMON 2012 (SouthEast Regional Meeting On Numbers) held at Western Carolina University March 30 - April 1, 2012.
