منابع مشابه
Hamiltonicity in connected regular graphs
In 1980, Jackson proved that every 2-connected k-regular graph with at most 3k vertices is Hamiltonian. This result has been extended in several papers. In this note, we determine the minimum number of vertices in a connected k-regular graph that is not Hamiltonian, and we also solve the analogous problem for Hamiltonian paths. Further, we characterize the smallest connected k-regular graphs wi...
متن کاملHamiltonicity of regular 2-connected graphs
Let G be a k-regular 2-connected graph of order n. Jackson proved that G is hamiltonian if n 5 3k. Zhu and Li showed that the upper bound 3k on n can be relaxed to q k if G is 3-connected and k 2 63. We improve both results by showing that G is hamiltonian if n 5 gk 7 and G does not belong to a restricted class 3 of nonhamiltonian graphs of connectivity 2. To establish this result we obtain a v...
متن کاملHamiltonicity in 3-connected claw-free graphs
Kuipers and Veldman conjectured that any 3-connected claw-free graph with order ν and minimum degree δ ≥ ν+6 10 is Hamiltonian for ν sufficiently large. In this paper, we prove that if H is a 3-connected claw-free graph with sufficiently large order ν, and if δ(H) ≥ ν+5 10 , then either H is hamiltonian, or δ(H) = ν+5 10 and the Ryjác̆ek’s closure cl(H) of H is the line graph of a graph obtained...
متن کاملHamiltonicity of 3-connected line graphs
Thomassen conjectured that every 4-connected line graph is Hamiltonian. Lai et al. conjectured [H. Lai, Y. Shao, H. Wu, J. Zhou, Every 3-connected, essentially 11-connected line graph is Hamiltonian, J. Combin. Theory Ser. B 96 (2006) 571–576] that every 3-connected, essentially 4-connected line graph is Hamiltonian. In this note, we first show that the conjecture posed by Lai et al. is not tru...
متن کاملPlanar graphs, regular graphs, bipartite graphs and Hamiltonicity
by Derek Holton and Robert E. L. Aldred Department of Mathematics and Statistics University of Otago This paper seeks to review some ideas and results relating to Hamiltonian graphs. We list the well known results which are to be found in most undergraduate graph theory courses and then consider some old theorems which are fundamental to planar graphs. By restricting our attention to 3-connecte...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2013
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2013.08.005