The entire graph of a bridgeless connected plane graph is hamiltonian
نویسندگان
چکیده
منابع مشابه
The entire graph of a bridgeless connected plane graph is hamiltonian
In thw pq=wr WC \hcw thrtt the enttre graph of a bridgcle\s connected plane graph is hitm&wnlan. and thwt the entlrz pph of ti plane blwk IS hamiltonian connected and vertex p~~c~whc. In addition. WI: 4ww that in an); hhxk G which is not a circuit, given a vertex v of G and (4 TWUI~ k of G. there is a path p. suspen&d m fi, such that p is a path in k of iength at least I and ii .E(p) \:,(G E(p)...
متن کاملEvery 4-connected line graph of a quasi claw-free graph is hamiltonian connected
Let G be a graph. For any two distinct vertices x and y in G, denote distG(x, y) the distance in G from x and y. For u, v ∈ V (G) with distG(u, v) = 2, denote JG(u, v) = {w ∈ NG(u)∩NG(v)|N(w) ⊆ N [u]∪ N [v]}. A graph G is claw-free if it contains no induced subgraph isomorphic to K1,3. A graph G is called quasi-claw-free if JG(u, v) 6= ∅ for any u, v ∈ V (G) with distG(u, v) = 2. Kriesell’s res...
متن کاملEvery 3-connected, essentially 11-connected line graph is Hamiltonian
Thomassen conjectured that every 4-connected line graph is Hamiltonian. A vertex cut X of G is essential if G−X has at least two non-trivial components. We prove that every 3-connected, essentially 11-connected line graph is Hamiltonian. Using Ryjác̆ek’s line graph closure, it follows that every 3-connected, essentially 11-connected claw-free graph is Hamiltonian. © 2005 Elsevier Inc. All rights...
متن کاملEvery 3-connected claw-free Z8-free graph is Hamiltonian
In this article, we first show that every 3-edge-connected graph with circumference at most 8 is supereulerian, which is then applied to show that a 3-connected claw-free graph without Z8 as an induced subgraph is Hamiltonian, where Z8 denotes the graph derived from identifying one end vertex of P9 (a path with 9 vertices) with one vertex of a triangle. The above two results are both best possi...
متن کاملdynamic coloring of graph
در این پایان نامه رنگ آمیزی دینامیکی یک گراف را بیان و مطالعه می کنیم. یک –kرنگ آمیزی سره ی رأسی گراف g را رنگ آمیزی دینامیکی می نامند اگر در همسایه های هر رأس v?v(g) با درجه ی حداقل 2، حداقل 2 رنگ متفاوت ظاهر شوند. کوچکترین عدد صحیح k، به طوری که g دارای –kرنگ آمیزی دینامیکی باشد را عدد رنگی دینامیکی g می نامند و آنرا با نماد ?_2 (g) نمایش می دهند. مونت گمری حدس زده است که تمام گراف های منتظم ...
15 صفحه اولذخیره 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: Discrete Mathematics
سال: 1976
ISSN: 0012-365X
DOI: 10.1016/0012-365x(76)90101-1