Cycles containing 12 vertices in 3-connected cubic graphs
S Bau, D Holton - Journal of graph theory, 1991 - dl.acm.org
S Bau, D Holton
Journal of graph theory, 1991•dl.acm.org… We establish that every cyclically 4-connected cubic planar graph of order at most 40 is
hamiltonian. Furthermore, this bound is determined to be sharp, and we present all
nonhamiltonian examples of order 42. In addition we list all nonhamiltonian ... … Let G n be
a class of graphs on n vertices. For an integer c, let ex(g n , c) be the smallest integer such
that if G is a graph in G n with more than ex(G n , c) edges, then G contains a cycle of length
more than c. A classical result of Erdös and Gallai is ... …
hamiltonian. Furthermore, this bound is determined to be sharp, and we present all
nonhamiltonian examples of order 42. In addition we list all nonhamiltonian ... … Let G n be
a class of graphs on n vertices. For an integer c, let ex(g n , c) be the smallest integer such
that if G is a graph in G n with more than ex(G n , c) edges, then G contains a cycle of length
more than c. A classical result of Erdös and Gallai is ... …
Abstract
A total dominating set in a graph G is a set S of vertices of G such that every vertex in G is adjacent to a vertex in S. Recently, the following question was proposed:
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