23,679 research outputs found
On minimum degree conditions for supereulerian graphs
A graph is called supereulerian if it has a spanning closed trail. Let be a 2-edge-connected graph of order such that each minimal edge cut with satisfies the property that each component of has order at least . We prove that either is supereulerian or belongs to one of two classes of exceptional graphs. Our results slightly improve earlier results of Catlin and Li. Furthermore our main result implies the following strengthening of a theorem of Lai within the class of graphs with minimum degree : If is a 2-edge-connected graph of order with such that for every edge , we have , then either is supereulerian or belongs to one of two classes of exceptional graphs. We show that the condition cannot be relaxed
Matrix models without scaling limit
In the context of hermitean one--matrix models we show that the emergence of
the NLS hierarchy and of its reduction, the KdV hierarchy, is an exact result
of the lattice characterizing the matrix model. Said otherwise, we are not
obliged to take a continuum limit to find these hierarchies. We interpret this
result as an indication of the topological nature of them. We discuss the
topological field theories associated with both and discuss the connection with
topological field theories coupled to topological gravity already studied in
the literature.Comment: Latex, SISSA-ISAS 161/92/E
The (N,M)-th KdV hierarchy and the associated W algebra
We discuss a differential integrable hierarchy, which we call the (N, M)MW_N$ algebra. We show
that there exist M distinct reductions of the (N, M)--th KdV hierarchy, which
are obtained by imposing suitable second class constraints. The most drastic
reduction corresponds to the (N+M)--th KdV hierarchy. Correspondingly the W(N,
M) algebra is reduced to the W_{N+M} algebra. We study in detail the
dispersionless limit of this hierarchy and the relevant reductions.Comment: 40 pages, LaTeX, SISSA-171/93/EP, BONN-HE-46/93, AS-IPT-49/9
On stability of the Hamiltonian index under contractions and closures
The hamiltonian index of a graph is the smallest integer such that the -th iterated line graph of is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an -contractible subgraph of a graph nor the closure operation performed on (if is claw-free) affects the value of the hamiltonian index of a graph
Toughness and hamiltonicity in -trees
We consider toughness conditions that guarantee the existence of a hamiltonian cycle in -trees, a subclass of the class of chordal graphs. By a result of Chen et al.\ 18-tough chordal graphs are hamiltonian, and by a result of Bauer et al.\ there exist nontraceable chordal graphs with toughness arbitrarily close to . It is believed that the best possible value of the toughness guaranteeing hamiltonicity of chordal graphs is less than 18, but the proof of Chen et al.\ indicates that proving a better result could be very complicated. We show that every 1-tough 2-tree on at least three vertices is hamiltonian, a best possible result since 1-toughness is a necessary condition for hamiltonicity. We generalize the result to -trees for : Let be a -tree. If has toughness at least then is hamiltonian. Moreover, we present infinite classes of nonhamiltonian 1-tough -trees for each $k\ge 3
Fast Determination of Soil Behavior in the Capillary Zone Using Simple Laboratory Tests
INE/AUTC 13.1
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