# PUBLICATIONS

### Books:

Baniasadi, P., Ejov, V., Filar, J.A. and Haythorpe, M. “Genetic Theory for Cubic Graphs”. Switzerland: Springer Publishing Company, 2016. Springer

Avrachenkov, K.E., Filar, J.A. and Howlett, P.G. “Analytic Perturbation Theory and Its Applications.” SIAM, Philadelphia, 2013. SIAM EasyCart

Haythorpe, M. “Markov Chain Based Algorithms for the Hamiltonian Cycle Problem.” Scholars’ Press, Saarbrücken, 2013. Morebooks

Borkar, V.S., Ejov, V., Filar, J.A. and Nguyen, G.T. “Hamiltonian cycle problems and markov chains.” Series: *International Series in Operations Research and Management Science*, Springer, 2012. Springer

Eshragh, A. “Hamiltonian Cycles and the Space of Discounted Occupational Measure.” Lambert Academic Publishers, Saarbrücken, 2011.

### Book chapters:

Filar, J.A. and Haythorpe, M. “A Linearly-Growing Conversion from the Set Splitting Problem to the Directed Hamiltonian Cycle Problem.” In: *Optimization and Control Methods in Industrial Engineering and Construction*, Springer, Dordrecht, 2014. Springer

Filar, J.A. and Liu, K. “Hamiltonian cycle problem and singularly perturbed Markov decision process.” In: *Lecture Notes-Monograph Series*, Institute of Mathematical Statistics, pp 45-63, 1996. JSTOR

Chen, M. and Filar, J.A. “Hamiltonian cycles, quadratic programming, and ranking of extreme points.” In: *Recent advances in global optimization*, Princeton University Press, Princeton, pp 32-49, 1992. ACM Digital Library

### Journal articles:

Glynn, D., Haythorpe, M. and Moeini, A. Directed in-out graphs of optimal size. *Australasian Journal of Combinatorics*, 72(2):405–420, 2018. PDF available

Haythorpe, M. “FHCP challenge set: The first set of structurally difficult instances of the hamiltonian cycle problem.” *Bulletin of the ICA*, 83:98-107, 2018. PDF available

Ejov, V., Filar, J.A., Haythorpe, M., Roddick, J. and Rossomakhine, S. “A note on using the resistance-distance matrix to solve Hamiltonian cycle problem.” *Annals of Operations Research*, 261(1-2):393-399, 2018. SpringerLink

Filar, J.A., Haythorpe, M. and Taylor, R. “Linearly-growing reductions of Karp’s 21 NP-complete problems.” *Numerical Algebra, Control and Optimization*, 8(1):1-16, 2018. AIMS

Alahmadi, A.N. and Glynn, D.G. “Multiple Hamilton cycles in bipartite cubic graphs: An algebraic method.” *Finite Fields and Their Applications*, 44:18-21, 2017. ResearchGate

Haythorpe, M. “Reducing the generalised Sudoku problem to the Hamiltonian cycle problem.” *AKCE International Journal of Graphs and Combinatorics*, 13(3):272-282, 2016. ScienceDirect

Haythorpe, M. “Constructing arbitrarily large graphs with a specificed number of Hamiltonian cycles.” *Electronic Journal of Graph Theory and Applications*, 4(1):18-25, 2016. PDF available

Filar, J.A., Haythorpe, M. and Rossomakhine, S. “A new heuristic for detecting non-Hamiltonicity in cubic graphs.” *Computers and Operations Research*, 64:283-292, 2015. Elsevier

Filar, J.A. and Moeini, A. “Hamiltonian cycle curves in the space of discounted occupational measures.” *Annals of Operations Research*, accepted 2015, to appear. SpringerLink

Ejov, V., Haythorpe, M. and Rossomakhine, S. “A Linear-size Conversion of HCP to 3HCP.” *Australasian Journal of Combinatorics*, 62(1):45-58, 2015. PDF available

Baniasadi, P., Ejov, V., Filar, J.A., Haythorpe, M. and Rossomakhine, S. “Deterministic “Snakes and Ladders” Heuristic for the Hamiltonian Cycle Problem.” *Mathematical Programming Computation*, 6(1):55-75, 2014*. *SpringerLink

Haythorpe, M. “Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth”. *Universal Journal of Applied Mathematics*, 2(1):72-78, 2014. PDF available

Filar, J.A., Haythorpe, M. and Murray, W. “On the Determinant and its Derivatives of the Rank-one corrected Generator of a Markov Chain on a Graph.” *Journal of Global Optimization*, 56(4):1425-1440, 2013. SpringerLink

Eshragh, A., Filar, J.A. and Haythorpe, M. “A hybrid simulation-optimization algorithm for the Hamiltonian cycle problem.” *Annals of Operations Research*, 189(1):103-125, 2011. SpringerLink

Eshragh, A. and Filar, J.A. “Hamiltonian Cycles, Random Walks, and Discounted Occupational Measures.” *Mathematics of Operations Research*, 36(2):258-270, 2011. Informs Online

Borkar, V.S. and Filar, J.A. “Markov chains, Hamiltonian cycles and volumes of convex bodies.” *Journal of Global Optimization*, DOI 10.1007/s10898-011-9819-6, 2011. SpringerLink

Haythorpe, M. “Finding Hamiltonian cycles using an interior point method.” *Australian Mathematics Society Gazette*, 37:170-179, 2010. PDF available

Filar, J.A., Haythorpe, M. and Nguyen, G.T. “A conjecture on the prevalence of cubic bridge graphs.” *Discussiones Mathematicae Graph Theory*, 30(1):175-179, 2010. Manuscript available

Ejov, V., Filar, J.A., Haythorpe, M. and Nguyen, G.T. “Refined MDP-based branch-and-fix algorithm for the Hamiltonian Cycle Problem.” *Mathematics of Operations Research*, 34(3):758-768, 2009. ACM Digital Library

Ejov, V., Friedland, S. and Nguyen, G.T. “A note on the graph’s resolvent and the multifilar structure.” *Linear Algebra and its Applications*, 431(8):1367-1379, 2009. ScienceDirect

Ejov, V. and Nguyen, G.T. “Consistent behavior of certain perturbed determinants induced by graphs.” *Linear Algebra and its Applications*, 431(5-7):543-552, 2009. ScienceDirect

Borkar, V.S., Ejov, V. and Filar, J.A. “On the Hamiltonicity gap and doubly stochastic matrices.” *Random Structures and Algorithms*, 34(4):502-519, 2009. Wiley Online Library

Ejov, V., Filar, J.A., Murray, W. and Nguyen, G.T. “Determinants and longest cycles of graphs”. *SIAM Journal on Discrete Mathematics*, 22(3):1215-1225, 2008. SIAM

Ejov, V., Filar, J.A. and Spieksma, F.M. “On regularly perturbed fundamental matrices.” *Journal of Mathematical Analysis and Applications*, 336(1):18-30, 2007. ScienceDirect

Ejov, V., Filar, J.A., Lucas, S.K. and Zograf, P. “Clustering of spectra and fractals of regular graphs.” *Journal of Mathematical Analysis and Applications*, 333(1):236-246, 2007. ScienceDirect

Filar, J.A. “Controlled Markov chains, graphs, and Hamiltonicity.” *Foundations and Trends*®* in Stochastic Systems*, 1(2):77-162, 2006. ACM Digital Library

Ejov, V., Filar, J.A., Lucas, S.K. and Nelson, J.L. “Solving the Hamiltonian cycle problem using symbolic determinants.” *Taiwanese Journal of Mathematics*, 10(2):327-338, 2006. PDF available

Filar, J.A., Gupta, A. and Lucas, S.K. “Connected co-spectral graphs are not necessarily both Hamiltonian.” *Australian Mathematical Society Gazette*, 32(3):193, 2005. PDF available

Borkar, V.S., Ejov, V. and Filar, J.A. “Directed graphs, Hamiltonicity and doubly stochastic matrices.” *Random Structures and Algorithms*, 25(4):376-395, 2004. Wiley Online Library

Ejov, V., Filar, J.A. and Gondzio, J. “An interior point heuristic for the Hamiltonian cycle problem via Markov decision processes.” *Journal of Global Optimization*, 29(3):315-334, 2004. SpringerLink

Ejov, V., Filar, J.A. and Nguyen, M. “Hamiltonian Cycles and Singularly Perturbed Markov Chains”. *Mathematics of Operations Research*, 29(1):114-131, 2004. JSTOR

Ejov, V., Filar, J.A. and Thredgold, J. “Geometric interpretation of Hamiltonian cycles problem via singularly perturbed Markov decision processes.” *Optimization*, 52(4-5):441-458, 2003. Taylor & Francis Online

Filar, J.A. and Lasserre, J.B. “A non-standard branch and bound method for the Hamiltonian cycle problem.” *Australian and New Zealand Industrial and Applied Mathematics Journal*, 42:586-607, 2000. ANZIAM Journal

Andramonov, M., Filar, J.A., Pardalos, P. and Rubinov, A. “Hamiltonian cycle problem via Markov chains and min-type approaches.” *Nonconvex Optimization and its Applications*, 42:31-47, 2000. ScientificCommons

Feinberg, E. “Constrained discounted Markov decision processes and Hamiltonian cycles.” *Mathematics of Operations Research*, 25(1):130-140, 2000. JSTOR

Filar, J.A. and Krass, D. “Hamiltonian Cycles and Markov Chains.” *Mathematics of Operations Research*, 19(1):223-237, 1994. JSTOR

### PhD Theses

Clancy, K. “Detecting Non-Hamiltonian Graphs by Improved Linear Programs and Graph Reductions.” Flinders University, 2017. PDF available

Moeini, A. “Approximations of the Convex Hull of Hamiltonian Cycles for Cubic Graphs.” Flinders University, 2016. PDF available

Eshragh, A. “Hamiltonian cycles and the space of discounted occupational measures.” University of South Australia, 2011. Trove

Haythorpe, M. “Markov Chain based algorithms for the Hamiltonian cycle problem.” University of South Australia, 2010. Systems Optimization Laboratory

Nguyen, G.T. “Hamiltonian cycle problem, Markov decision processes and graph spectra.” University of South Australia, 2009.

Liu, K. “Theory and Applications of Markov Decision Processes and Their Perturbations”, University of South Australia,1997.

Chen, M. “Markov Decision Processes, Finite Approximations and Mathematical Programming.” University of Maryland Baltimore Country, 1992.

Krass, D. “Contributions to the Theory and Applications of Markov Processes.” The Johns Hopkins University, 1989.