Displaying similar documents to “On cubic planar hypohamiltonian and hypotraceable graphs.”

Note on Petrie and Hamiltonian cycles in cubic polyhedral graphs

Jaroslav Ivančo, Stanislav Jendroľ, Michal Tkáč (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this note we show that deciding the existence of a Hamiltonian cycle in a cubic plane graph is equivalent to the problem of the existence of an associated cubic plane multi-3-gonal graph with a Hamiltonian cycle which takes alternately left and right edges at each successive vertex, i.ei̇t is also a Petrie cycle. The Petrie Hamiltonian cycle in an n -vertex plane cubic graph can be recognized by an O ( n ) -algorithm.

Secure sets and their expansion in cubic graphs

Katarzyna Jesse-Józefczyk, Elżbieta Sidorowicz (2014)

Open Mathematics

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Consider a graph whose vertices play the role of members of the opposing groups. The edge between two vertices means that these vertices may defend or attack each other. At one time, any attacker may attack only one vertex. Similarly, any defender fights for itself or helps exactly one of its neighbours. If we have a set of defenders that can repel any attack, then we say that the set is secure. Moreover, it is strong if it is also prepared for a raid of one additional foe who can strike...