6,645 research outputs found
Long cycles in graphs with large degree sums and neighborhood unions
We present and prove several results concerning the length of longest cycles in 2-connected or 1-tough graphs with large degree sums. These results improve many known results on long cycles in these graphs. We also consider the sharpness of the results and discuss some possible strengthenings
Long cycles in graphs containing a 2-factor with many odd components
We prove a result on the length of a longest cycle in a graph on n vertices that contains a 2-factor and satisfies d(u)+d(c)+d(w)n+2 for every tiple u, v, w of independent vertices. As a corollary we obtain the follwing improvement of a conjectre of Häggkvist (1992): Let G be a 2-connected graph on n vertices where every pair of nonadjacent vertices has degree sum at least n-k and assume G has a 2-factor with at least k+1 odd components. Then G is hamiltonian
Pancyclicity of Hamiltonian line graphs
Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n), the line graph L(G) of G is pancyclic whenever L(G) is hamiltonian. Results are proved showing that f(n) = ®(n 1/3)
Formation of Double Neutron Stars, Millisecond Pulsars and Double Black Holes
The 1982 model for the formation of the Hulse-Taylor binary radio pulsar PSR
B1913+16 is described, which since has become the standard model for the
formation of double neutron stars, confirmed by the 2003 discovery of the
double pulsar system PSR J0737-3039AB. A brief overview is given of the present
status of our knowledge of the double neutron stars, of which 15 systems are
presently known. The binary-recycling model for the formation of millisecond
pulsars is described, as put forward independently by Alpar et al. (1982),
Radhakrishnan and Srinivasan (1982) and Fabian et al. (1983). This now is the
standard model for the formation of these objects, confirmed by the discovery
in 1998 of the accreting millisecond X-ray pulsars. It is noticed that the
formation process of close double black holes has analogies to that of close
double neutron stars, extended to binaries of larger iinitial component masses,
although there are also considerable differences in the physics of the binary
evolution at these larger masses.Comment: Has appeared in Journal of Astrophysics and Astronomy special issue
on 'Physics of Neutron Stars and Related Objects', celebrating the 75th birth
year of G. Srinivasa
Does bank capital matter for monetary transmission?
Paper for a conference sponsored by the Federal Reserve Bank of New York entitled Financial Innovation and Monetary TransmissionBank capital ; Monetary policy
A generalization of Ore's Theorem involving neighborhood unions
AbstractLet G be a graph of order n. Settling conjectures of Chen and Jackson, we prove the following generalization of Ore's Theorem: If G is 2-connected and |N(u)∪N(v)|⩾12n for every pair of nonadjacent vertices u,v, then either G is hamiltonian, or G is the Petersen graph, or G belongs to one of three families of exceptional graphs of connectivity 2
Long cycles, degree sums and neighborhood unions
AbstractFor a graph G, define the parameters α(G)=max{|S| |S is an independent set of vertices of G}, σk(G)=min{∑ki=1d(vi)|{v1,…,vk} is an independent set} and NCk(G)= min{|∪ki=1 N(vi)∥{v1,…,vk} is an independent set} (k⩾2). It is shown that every 1-tough graph G of order n⩾3 with σ3(G)⩾n+r⩾n has a cycle of length at least min{n,n+NCr+5+∈(n+r)(G)-α(G)}, where ε(i)=3(⌈13i⌉−13i). This result extends previous results in Bauer et al. (1989/90), Faßbender (1992) and Flandrin et al. (1991). It is also shown that a 1-tough graph G of order n⩾3 with σ3(G)⩾n+r⩾n has a cycle of length at least min{n,2NC⌊18(n+6r+17)⌋(G)}. Analogous results are established for 2-connected graphs
Long Gamma-Ray Burst Progenitors: Boundary Conditions and Binary Models
The observed association of Long Gamma-Ray Bursts (LGRBs) with peculiar Type
Ic supernovae gives support to Woosley`s collapsar/hypernova model, in which
the GRB is produced by the collapse of the rapidly rotating core of a massive
star to a black hole. The association of LGRBs with small star-forming galaxies
suggests low-metallicity to be a condition for a massive star to evolve to the
collapsar stage. Both completely-mixed single star models and binary star
models are possible. In binary models the progenitor of the GRB is a massive
helium star with a close companion. We find that tidal synchronization during
core-helium burning is reached on a short timescale (less than a few
millennia). However, the strong core-envelope coupling in the subsequent
evolutionary stages is likely to rule out helium stars with main-sequence
companions as progenitors of hypernovae/GRBs. On the other hand, helium stars
in close binaries with a neutron-star or black-hole companion can, despite the
strong core-envelope coupling in the post-helium burning phase, retain
sufficient core angular momentum to produce a hypernova/GRB.Comment: 8 pp., 2 figs, Proceedings of 5th Stromlo Symposiu
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