Research
My research interests lie primarily in the areas of graph theory (the study of dots and lines), discrete mathematics (the study of things you can count), and combinatorics (the study of counting). I am particularly interested in graph colorings, cycle structure in graphs, saturation-type problems, and directed graphs.
If you're a student and you're interested in working with me or learning more about what I'm interested in, send me an email or watch the video below! It's a talk I gave at GRCC in Jan. 2018 (you can skip to the 9 minute mark to get to the math, since I talk about my background for the first few minutes).
Accepted and Published Papers
X. Liu, M. Santana, and T. Short, Every subcubic multigraph is (1, 2^7)-packing edge-colorable, J. Graph Theory (to appear).
M. Santana and M. Van Bonn, Sharp minimum degree conditions for disjoint doubly chorded cycles, J. Comb (to appear).
T. Molla and M. Santana, Disjoint cycles in graphs with restricted independence number, Discrete Appl. Math. 320 (2022), 95 - 105.
E. Marshall and M. Santana, Sharp minimum degree conditions for the existence of disjoint theta graphs, Electron. J. Combin. 28 (2021), no. 3, Paper 3.50.
J. Carraher, M. Ferrara, T. Morris, and M. Santana, Characterizing forbidden subgraphs that imply pancyclicity in 4-connected, claw-free graphs, Discrete Math. 344 (2021), no. 10, 112522.
T. Molla, M. Santana, and E. Yeager, Disjoint cycles and chorded cycles in a graph with given minimum degree, Discrete Math. 343 (2020), no. 6.
M. Huang, M. Santana, and G. Yu, Strong chromatic index of graphs with maximum degree four, Electron. J. Combin. 25 (2018), no. 3, Paper 3.31. arxiv
C. Erbes, T. Molla, S. Mousely, and M. Santana, Spanning trees with leaf distance at least d, Discrete Math. 340 (2017), no. 6, 1412 - 1418.
T. Molla, M. Santana, and E. Yeager, A refinement of theorems on vertex-disjoint chorded cycles, Graphs Combin. 33 (2017), no. 2, 181 - 201. arxiv
S. Behrens, C. Erbes, M. Santana, D. Yager, and E. Yeager, Graphs with induced saturation number zero, Electron. J. Combin. 23 (2016), no. 1, Paper 1.54. arxiv
A. V. Kostochka, X. Li, W. Ruksasakchai, M. Santana, T. Wang, and G. Yu, The strong chromatic index of subcubic planar multigraphs is at most nine, European J. Combin 51 (2016), 380-397. arxiv
K.B. Reid and M. Santana, Landau's theorem revisited again, J. Combin. Math. Combin. Comput. 80 (2012), 171 - 191. (invited paper in honor of Ralph Stanton). arxiv
M. Santana, Two investigations on tournaments: intersection spectra and score sequences (2011) (Masters Thesis).