2,869 research outputs found
Tilings of quadriculated annuli
Tilings of a quadriculated annulus A are counted according to volume (in the
formal variable q) and flux (in p). We consider algebraic properties of the
resulting generating function Phi_A(p,q). For q = -1, the non-zero roots in p
must be roots of unity and for q > 0, real negative.Comment: 33 pages, 12 figures; Minor changes were made to make some passages
cleare
Finding a Maximum 2-Matching Excluding Prescribed Cycles in Bipartite Graphs
We introduce a new framework of restricted 2-matchings close to Hamilton cycles. For an undirected graph (V,E) and a family U of vertex subsets, a 2-matching F is called U-feasible if, for each setU in U, F contains at most |setU|-1 edges in the subgraph induced by U. Our framework includes C_{= 5. For instance, in bipartite graphs in which every cycle of length six has at least two chords, our algorithm solves the maximum C_{<=6}-free 2-matching problem in O(n^2 m) time, where n and m are the numbers of vertices and edges, respectively
Phase transitions of extremal cuts for the configuration model
The -section width and the Max-Cut for the configuration model are shown
to exhibit phase transitions according to the values of certain parameters of
the asymptotic degree distribution. These transitions mirror those observed on
Erd\H{o}s-R\'enyi random graphs, established by Luczak and McDiarmid (2001),
and Coppersmith et al. (2004), respectively
Minimal-area metrics on the Swiss cross and punctured torus
The closed string field theory minimal-area problem asks for the conformal
metric of least area on a Riemann surface with the condition that all
non-contractible closed curves have length at least 2\pi. Through every point
in such a metric there is a geodesic that saturates the length condition, and
saturating geodesics in a given homotopy class form a band. The extremal metric
is unknown when bands of geodesics cross, as it happens for surfaces of
non-zero genus. We use recently proposed convex programs to numerically find
the minimal-area metric on the square torus with a square boundary, for various
sizes of the boundary. For large enough boundary the problem is equivalent to
the "Swiss cross" challenge posed by Strebel. We find that the metric is
positively curved in the two-band region and flat in the single-band regions.
For small boundary the metric develops a third band of geodesics wrapping
around it, and has both regions of positive and negative curvature. This
surface can be completed to provide the minimal-area metric on a once-punctured
torus, representing a closed-string tadpole diagram.Comment: 59 pages, 41 figures. v2: Minor edits and reference update
Hamilton cycles in 5-connected line graphs
A conjecture of Carsten Thomassen states that every 4-connected line graph is
hamiltonian. It is known that the conjecture is true for 7-connected line
graphs. We improve this by showing that any 5-connected line graph of minimum
degree at least 6 is hamiltonian. The result extends to claw-free graphs and to
Hamilton-connectedness
Listing minimal edge-covers of intersecting families with applications to connectivity problems
AbstractLet G=(V,E) be a directed/undirected graph, let s,t∈V, and let F be an intersecting family on V (that is, X∩Y,X∪Y∈F for any intersecting X,Y∈F) so that s∈X and t∉X for every X∈F. An edge set I⊆E is an edge-cover of F if for every X∈F there is an edge in I from X to V−X. We show that minimal edge-covers of F can be listed with polynomial delay, provided that, for any I⊆E the minimal member of the residual family FI of the sets in F not covered by I can be computed in polynomial time. As an application, we show that minimal undirected Steiner networks, and minimal k-connected and k-outconnected spanning subgraphs of a given directed/undirected graph, can be listed in incremental polynomial time
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