Research Interests: Ramsey Theory,
Hypergraphs, Extremal Combinatorics, and Algebraic Number
Theory
Books:
M. Budden, Star-Critical
Ramsey Numbers for Graphs, SpringerBriefs in
Mathematics, Springer, Cham, 2023.
M. Budden, Weakened
Ramsey Theory, CRC Press, Boca Raton, 2026.
Research Articles (*
indicates undergraduate student coauthor, ** indicates
graduate student coauthor):
[1] M. Budden, Local Coefficient Matrices of
Metaplectic Groups, Journal of
Lie Theory 16 (2006), 239-249. pdf
[2] M. Budden, P. Hadavas, L. Hoffman, and
C. Pretz, Generating Valid
4×4 Correlation Matrices, Applied
Mathematics E-Notes 7 (2007), 53-59. pdf
[3] M. Budden, R.J. Eisenmenger*, and J. Kish**, A Generalization of Scholz's
Reciprocity Law, Journal de Théorie
des Nombres de Bordeaux 19 (2007), 583-594. pdf
[4] M. Budden, P. Hadavas, and L. Hoffman,
On the Generation of
Correlation Matrices, Applied
Mathematics E-Notes 8 (2008), 279-282. pdf
[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 Università 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
[54]
M. Budden and
E. DeJonge, The
3-Color
2-Chromatic
Gallai-Ramsey
Number for
Complete
Graphs, under
review.
Articles
in Preparation (* indicates undergraduate student
coauthor, ** indicates graduate student coauthor):
[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.
Math Links:
Videos on
Ramsey Theory
Mathematics arXiv
Mathematics
Genealogy Project
The Institute
of Combinatorics and its Applications
Number
Theory Web
