Displaying similar documents to “Dualizing cubic graph theory”

Mácajová and Škoviera conjecture on cubic graphs

Jean-Luc Fouquet, Jean-Marie Vanherpe (2010)

Discussiones Mathematicae Graph Theory

Similarity:

A conjecture of Mácajová and Skoviera asserts that every bridgeless cubic graph has two perfect matchings whose intersection does not contain any odd edge cut. We prove this conjecture for graphs with few vertices and we give a stronger result for traceable graphs.

On generating snarks

Busiso P. Chisala (1998)

Discussiones Mathematicae Graph Theory

Similarity:

We discuss the construction of snarks (that is, cyclically 4-edge connected cubic graphs of girth at least five which are not 3-edge colourable) by using what we call colourable snark units and a welding process.

Secure sets and their expansion in cubic graphs

Katarzyna Jesse-Józefczyk, Elżbieta Sidorowicz (2014)

Open Mathematics

Similarity:

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...