# Vaidy Sivaraman

I am an assistant professor in the department of mathematics and statistics at Mississippi State University. (https://www.math.msstate.edu)

My main interest is in graph theory: Graph invariants, induced subgraphs, chi-boundedness, graph-matroid symbiosis, signed graphs.

I received my Ph.D. from The Ohio State University in December 2012. My dissertation “Some topics concerning graphs, signed graphs, and matroids” was supervised by Prof. Neil Robertson. (I was his last (22) Ph.D. student.)

Email:

Research Interests: Graph Theory (structural and algorithmic aspects, induced subgraphs, graph invariants, chi-boundedness), Signed Graphs, Matroid Theory

Particular topics of interest include well-quasi-ordering, graph invariants (particularly chromatic number, Hadwiger number, girth), minor-closed classes of graphs, induced subgraphs, signed graphs, matroids coming from graphs, signed-graphic matroids, and statistical properties of matroids.

Publications:

1. Two short proofs of the bounded case of S. B. Rao's degree sequence conjecture, Discrete Math. 313 (2013), no. 13, 1500-1501.

2. Bicircular signed-graphic matroids, Discrete Math. 328 (2014), 1–4.

3. A unified proof of Brooks’ theorem and Catlin’s theorem, Discrete Math. 338 (2015) no. 2, 272–273.

4. (with John Maharry, Neil Robertson, and Daniel Slilaty) Flexibility of projective-planar embeddings, J. Combin. Theory Ser. B 122 (2017), 241–300.

5. Some problems on induced subgraphs, Discrete Applied Mathematics, 236 (2018) 422-427.

6. (with Maria Chudnovsky) Odd holes in bull-free graphs, SIAM J. Discrete Math. 32 (2018), no. 2, 951–955.

7. (with Richard Behr, Thomas Zaslavsky) Mock threshold graphs, Discrete Math. 341 (2018) 2159–2178.

8. (with Maria Chudnovsky) Perfect divisibility and 2-divisibility, J. Graph Theory 90 (2019) 54-60.

9. (with Bart Litjens, Sven Polak) Sum-perfect graphs, Discrete Applied Mathematics, 259 (2019) 232-239.

10. An application of the Gyarfas path argument, Discrete Math. 342 (2019) 2306-2307.

11. (with Daniel Slilaty) The graphs that have antivoltages using groups of small order, Discrete Math. 342 (2019) 2951–2965.

12. (with Ringi Kim, O-joung Kwon, Sang-il Oum) Classes of graphs with no long cycle as a vertex-minor are polynomially 𝜒-bounded, J. Combin. Theory Ser. B. 140 (2020) 372-386.

13. (with Katie Cameron, Shenwei Huang, Irena Penev) The class of (P7,C4,C5)-free graphs: decomposition, chi-boundedness, algorithms, J. Graph Theory 93 (2020) 503-552.

14. (with Dan Slilaty) The family of bicircular matroids closed under duality, Graphs Combin. 38, Article number 24 (2022).

15. (with Thomas Zaslavsky) Two Hamiltonian cycles, Discrete Math. 345 (2022), article 112797.

16. (with T. Karthick, Jenny Kaufmann) Coloring graph classes with no induced fork via perfect divisibility, The Electronic Journal of Combinatorics, P3.19 (2022).

17. (with Mohammed A. Mutar, Daniel Slilaty) Signed Ramsey numbers, Graphs Combin. 40, Article number 9 (2024).

18. (with Daniel Slilaty) Line graphs of directed graphs I, to appear in Trans. Comb.

19. (with Ahmad Asiri) Tangled and sign-symmetric signed graphs, submitted.

20. (with Ahmad Asiri) Signings of the complete graph on six vertices with an edge deleted, submitted.

21. (with Jagdeep Singh and Thomas Zaslavsky) Apex graphs and cographs, submitted.

22. (with Rebecca Whitman) Hereditary Nordhaus-Gaddum graphs, submitted.

Arxiv: http://arxiv.org/find/math/1/au:+Sivaraman_V/0/1/0/all/0/1

Current projects include understanding some hereditary classes of graphs, coloring perfect graphs, chi-boundedness, line graphs of directed graphs, antivoltages in graphs, and the ubiquitous Tutte polynomial.

In preparation:

1. (with Bart Litjens, Sven Polak, Bart Sevenster) A characterization of graphs with Dilworth number at most 3.

2. (with Thomas Zaslavsky) Smock (special mock threshold) graphs.

3. (with Thomas Zaslavsky) The seven signed Heawood graphs.

4. (with Jan Goedgebeur, Pierre Hauweele) Towards the forbidden induced subgraph characterization for graphs that have a connected dominating set of size 4.

5. The symmetrization operator on hereditary graph classes.

6. Pseudo-line graphs.

7. Some problems on the cop number of a graph.

8. On a relationship between the chromatic number and the number of spanning trees.

Coauthors:

1. Neil Robertson https://math.osu.edu/people/robertson.7

2. John Maharry https://u.osu.edu/maharry.1/

3. Daniel Slilaty http://www.wright.edu/~daniel.slilaty/

4. Maria Chudnovsky https://web.math.princeton.edu/~mchudnov/

5. Thomas Zaslavsky https://www2.math.binghamton.edu/p/people/zaslav/start

6. Richard Behr https://www2.math.binghamton.edu/p/people/grads/behr/start

7. Bart Litjens https://sites.google.com/site/bmlitjens/home

8. Sven Polak https://sites.google.com/site/svenpolak/

9. Kathie Cameron https://www.wlu.ca/academics/faculties/faculty-of-science/faculty-profiles/kathie-cameron/index.html

10. Shenwei Huang https://www.researchgate.net/profile/Shenwei_Huang2

11. Irena Penev https://iuuk.mff.cuni.cz/~ipenev/

12. Lex Schrijver https://homepages.cwi.nl/~lex/

13. Bart Sevenster https://sites.google.com/site/websitebartsevenster/

14. Stephen Testa https://www.linkedin.com/in/stephen-testa-69101b152

15. Sang-il Oum https://dimag.ibs.re.kr/home/sangil/

16. Ringi Kim, https://sites.google.com/view/ringikim/home

17. O-joung Kwon http://ojkwon.com

Member of organizing committe:https://sciences.ucf.edu/math/cumberland/

Member of organizing committee: http://msdiscretemath.org/2019/

Recent talks:

Joint Math Meeting, San Francisco, January 3, 2024

Mathematics Seminar, Mississippi State University, November 9, 2023

Combinatorics Seminar, University of Mississippi, November 1, 2023

AMS session on Recent Trends in Graph Theory, October 15, 2023

AMS session on Advances in Extremal Combinatorics, October 14, 2023

Combinatorics Seminar, University of California, Berkeley, May 4, 2023

Mathematics Seminar Series, Mississippi State University, March 24, 2023

Discrete Math seminar, Illinois State University, February 2022

New York Combinatorics seminar, October 2021

Atlanta Lecture Series in Combinatorics and Graph Theory (ALS 25), August 2021

Combinatorics seminar, Binghamton University, April 2021

Combinatorics seminar, Binghamton University, Nov 2020

Workshop on structure and coloring, BIRS, Banff, March 2020 (online)

Combinatorics seminar, University of Mississippi, Nov 2019

AMS Special session for Tom Zaslavsky, Binghamton, Oct 2019

SIAM Discrete math meeting, Vancouver, May 2019

Problems on cop number, short presentation in Barbados Graph Theory Workshop, Barbados, March 2019

Colloquium, Augusta University, February 2019

Colloquium, Mississippi State University, January 2019

International Conference on Graph Theory, Lyon, July 2018

Combinatorics seminar, University of Amsterdam, June 2018

Combinatorics seminar, University of Central Florida, March 2018

AMS special session for Neil Robertson, Ohio State, March 2018

Graph theorists working on induced subgraphs

Paul Seymour

Maria Chudnovsky

Alex Scott

Sophie Spirkl

Vasek Chvatal

Kristina Vuskovic

Nicolas Trotignon

Stephan Thomasse

Vadim Lozin

Martin Golumbic

Frederic Maffray (deceased)

Daniel Paulusma

Konrad Dabrowski

Chinh T. Hoang

Kathie Cameron

Shenwei Huang

T. Karthick

Andras Brandstadt

Raffaele Mosca

Dieter Kratsch

Van Bang Le

Ingo Scheiermeyer

Bert Randerath

Martin Milanic