The Parity Hamiltonian Cycle Problem in Directed Graphs

2016 ◽  
pp. 50-58
Author(s):  
Hiroshi Nishiyama ◽  
Yukiko Yamauchi ◽  
Shuji Kijima ◽  
Masafumi Yamashita
Keyword(s):  
Hamiltonian Cycle ◽  
Directed Graphs ◽  
Hamiltonian Cycle Problem

scholarly journals An Effective Algorithm for and Phase Transitions of the Directed Hamiltonian Cycle Problem

2010 ◽  
Vol 39 ◽  
pp. 663-687 ◽  
Author(s):  
G. Jäger ◽  
W. Zhang
Keyword(s):  
Phase Transitions ◽  
Hamiltonian Cycle ◽  
Directed Graphs ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Effective Algorithm ◽  
Intrinsic Properties ◽  
Award Winning ◽  
Close Relationship ◽  
Hamiltonian Cycle Problem

The Hamiltonian cycle problem (HCP) is an important combinatorial problem with applications in many areas. It is among the first problems used for studying intrinsic properties, including phase transitions, of combinatorial problems. While thorough theoretical and experimental analyses have been made on the HCP in undirected graphs, a limited amount of work has been done for the HCP in directed graphs (DHCP). The main contribution of this work is an effective algorithm for the DHCP. Our algorithm explores and exploits the close relationship between the DHCP and the Assignment Problem (AP) and utilizes a technique based on Boolean satisfiability (SAT). By combining effective algorithms for the AP and SAT, our algorithm significantly outperforms previous exact DHCP algorithms, including an algorithm based on the award-winning Concorde TSP algorithm. The second result of the current study is an experimental analysis of phase transitions of the DHCP, verifying and refining a known phase transition of the DHCP.

scholarly journals Semi-Degree Threshold for Anti-Directed Hamiltonian Cycles

10.37236/3610 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Louis DeBiasio ◽  
Theodore Molla
Keyword(s):  
Directed Graph ◽  
Hamiltonian Cycle ◽  
Minimum Degree ◽  
Directed Graphs ◽  
Hamiltonian Cycles ◽  
Alternate Direction ◽  
Degree Conditions

In 1960 Ghouila-Houri extended Dirac's theorem to directed graphs by proving that if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $n/2$, then $D$ contains a directed Hamiltonian cycle. For directed graphs one may ask for other orientations of a Hamiltonian cycle and in 1980 Grant initiated the problem of determining minimum degree conditions for a directed graph $D$ to contain an anti-directed Hamiltonian cycle (an orientation in which consecutive edges alternate direction). We prove that for sufficiently large even $n$, if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $\frac{n}{2}+1$, then $D$ contains an anti-directed Hamiltonian cycle. In fact, we prove the stronger result that $\frac{n}{2}$ is sufficient unless $D$ is one of two counterexamples. This result is sharp.

scholarly journals Solving SAT and Hamiltonian Cycle Problem Using Asynchronous P Systems

2012 ◽  
Vol E95-D (3) ◽  
pp. 746-754 ◽  
Author(s):  
Hirofumi TAGAWA ◽  
Akihiro FUJIWARA
Keyword(s):  
Hamiltonian Cycle ◽  
P Systems ◽  
Hamiltonian Cycle Problem

scholarly journals The Minimum Flow Cost Hamiltonian Cycle Problem: A comparison of formulations

2015 ◽  
Vol 187 ◽  
pp. 140-154 ◽  
Author(s):  
Camilo Ortiz-Astorquiza ◽  
Ivan Contreras ◽  
Gilbert Laporte
Keyword(s):  
Hamiltonian Cycle ◽  
Minimum Flow ◽  
Hamiltonian Cycle Problem

Heuristic approaches for the Minimum Labelling Hamiltonian Cycle Problem

2006 ◽  
Vol 25 ◽  
pp. 131-138 ◽  
Author(s):  
R. Cerulli ◽  
P. Dell'Olmo ◽  
M. Gentili ◽  
A. Raiconi
Keyword(s):  
Hamiltonian Cycle ◽  
Heuristic Approaches ◽  
Hamiltonian Cycle Problem
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