منابع مشابه
Counterexamples to the Cubic Graph Domination Conjecture
Let v(G) and γ(G) denote the number of vertices and the domination number of a graph G, respectively, and let ρ(G) = γ(G)/v(G). In 1996 B. Reed conjectured that ifG is a cubic graph, then γ(G) ≤ ⌈v(G)/3⌉. In 2005 A. Kostochka and B. Stodolsky disproved this conjecture for cubic graphs of connectivity one and maintained that the conjecture may still be true for cubic 2-connected graphs. Their mi...
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Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark’s conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) an...
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In 1995, Paul Erdős and András Gyárfás conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer m such that G contains a simple cycle of length 2m. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.
متن کاملHoffmann-Ostenhof's conjecture for traceable cubic graphs
It was conjectured by Hoffmann-Ostenhof that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. In this paper, we show that this conjecture holds for traceable cubic graphs. keywords: Cubic graph, Hoffmann-Ostenhof’s Conjecture, Traceable AMS Subject Classification: 05C45, 05C70
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2008
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2008.10128871