Nonhamiltonian 3-Connected Cubic Planar Graphs
نویسندگان
چکیده
منابع مشابه
Nonhamiltonian 3-Connected Cubic Planar Graphs
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 such graphs of order 42. In addition we list all nonhamiltonian cyclically 5-connected cubic planar graphs of order at most 52 and all nonhamiltonian 3-connected cubic planar graphs of girth 5 on at most 46 vert...
متن کاملCycles Through 23 Vertices in 3-Connected Cubic Planar Graphs
We establish that if A is a set of at most 23 vertices in a 3-connected cubic planar graph G, then there is a cycle in G containing A. This result is sharp. AMS Classification: 05C38 Let G be a 3-connected cubic planar graph and let A ⊆ V (G). It was shown in [4] that if |A| ≤ 19 there is a cycle C in G such that A ⊆ V (C). In this paper we show that if |A| ≤ 23, then G contains a cycle through...
متن کاملEdge bounds in nonhamiltonian k-connected graphs
Let G be a k-connected graph of order n with |E(G)|>(n−k 2 )+ k2. Then for (k = 1, n 3), (k = 2, n 10), and (k = 3, n 16), G is hamiltonian. The bounds are tight and for k = 1, (k = 2, n 12), and (k = 3, n 18) the extremal graphs are unique. A general bound will also be given for the number of edges in a nonhamiltonian k-connected graph, but the bound is not tight. © 2006 Elsevier B.V. All righ...
متن کاملPoint sets with planar embeddings of cubic, connected graphs
Let P be a set of n ≥ 3 points in the plane in general position with n even and let h being the number of points on the convex hull of P . We want to know in which cases P admits a planar embedding of a cubic, connected graph (a “cubic embedding”)? García et al. proved in [1] that cubic embeddings always exists for h ≤ 4n, but for higher values of h the question remained open. We present a char...
متن کاملGenerating unlabeled connected cubic planar graphs uniformly at random
We present an expected polynomial time algorithm to generate an unlabeled connected cubic planar graph uniformly at random. We first consider rooted connected cubic planar graphs, i.e., we count connected cubic planar graphs up to isomorphisms that fix a certain directed edge. Based on decompositions along the connectivity structure, we derive recurrence formulas for the exact number of rooted ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2000
ISSN: 0895-4801,1095-7146
DOI: 10.1137/s0895480198348665