846 research outputs found
On hypohamiltonian snarks and a theorem of Fiorini
In 2003, Cavicchioli et al. corrected an omission in the statement and proof of Fiorini's theorem from 1983 on hypohamiltonian snarks. However, their version of this theorem contains an unattainable condition for certain cases. We discuss and extend the results of Fiorini and Cavicchioli et al. and present a version of this theorem which is more general in several ways. Using Fiorini's erroneous result, Steffen had shown that hypohamiltonian snarks exist for some orders n >= 10 and each even n >= 92. We rectify Steffen's proof by providing a correct demonstration of a technical lemma on flower snarks, which might be of separate interest. We then strengthen Steffen's theorem to the strongest possible form by determining all orders for which hypohamiltonian snarks exist. This also strengthens a result of Macajova and Skoviera. Finally, we verify a conjecture of Steffen on hypohamiltonian snarks up to 36 vertices
Martingale approach to stochastic differential games of control and stopping
We develop a martingale approach for studying continuous-time stochastic
differential games of control and stopping, in a non-Markovian framework and
with the control affecting only the drift term of the state-process. Under
appropriate conditions, we show that the game has a value and construct a
saddle pair of optimal control and stopping strategies. Crucial in this
construction is a characterization of saddle pairs in terms of pathwise and
martingale properties of suitable quantities.Comment: Published in at http://dx.doi.org/10.1214/07-AOP367 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Polyhedra with few 3-cuts are hamiltonian
In 1956, Tutte showed that every planar 4-connected graph is hamiltonian. In
this article, we will generalize this result and prove that polyhedra with at
most three 3-cuts are hamiltonian. In 2002 Jackson and Yu have shown this
result for the subclass of triangulations. We also prove that polyhedra with at
most four 3-cuts have a hamiltonian path. It is well known that for each non-hamiltonian polyhedra with 3-cuts exist. We give computational
results on lower bounds on the order of a possible non-hamiltonian polyhedron
for the remaining open cases of polyhedra with four or five 3-cuts.Comment: 21 pages; changed titl
Every graph occurs as an induced subgraph of some hypohamiltonian graph
We prove the titular statement. This settles a problem of Chvátal from 1973 and encompasses earlier results of Thomassen, who showed it for K_3, and Collier and Schmeichel, who proved it for bipartite graphs. We also show that for every outerplanar graph there exists a planar hypohamiltonian graph containing it as an induced subgraph
On almost hypohamiltonian graphs
A graph is almost hypohamiltonian (a.h.) if is non-hamiltonian, there
exists a vertex in such that is non-hamiltonian, and is
hamiltonian for every vertex in . The second author asked in [J.
Graph Theory 79 (2015) 63--81] for all orders for which a.h. graphs exist. Here
we solve this problem. To this end, we present a specialised algorithm which
generates complete sets of a.h. graphs for various orders. Furthermore, we show
that the smallest cubic a.h. graphs have order 26. We provide a lower bound for
the order of the smallest planar a.h. graph and improve the upper bound for the
order of the smallest planar a.h. graph containing a cubic vertex. We also
determine the smallest planar a.h. graphs of girth 5, both in the general and
cubic case. Finally, we extend a result of Steffen on snarks and improve two
bounds on longest paths and longest cycles in polyhedral graphs due to
Jooyandeh, McKay, {\"O}sterg{\aa}rd, Pettersson, and the second author.Comment: 18 pages. arXiv admin note: text overlap with arXiv:1602.0717
Goal Programming as a Decision Model for Performance-Based Budgeting
AbstractThe spreadsheet applications are becoming a widely used tool for processing quantitative data and developing analytical solutions. The ability to build decision support systems (DSS) based on these spreadsheet solutions can facilitate knowledge management and increase information utilization within an organization. The paper describes the use of a spreadsheet solution to partially implement the performance-based budgeting (PB) principles for a public body. The solution builds on the goal programming optimization method and is exemplified for some real data
Every point is critical
We show that, for any compact Alexandrov surface S (without boundary) and any point y in S, there exists a point x in S for which y is a critical point. Moreover, we prove that uniqueness characterizes the surfaces homeomorphic to the sphere among smooth orientable surfaces. © 2013
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