509 research outputs found
An extensive English language bibliography on graph theory and its applications, supplement 1
Graph theory and its applications - bibliography, supplement
Computation of Contour Integrals on
Contour integrals of rational functions over , the moduli
space of -punctured spheres, have recently appeared at the core of the
tree-level S-matrix of massless particles in arbitrary dimensions. The contour
is determined by the critical points of a certain Morse function on . The integrand is a general rational function of the puncture
locations with poles of arbitrary order as two punctures coincide. In this note
we provide an algorithm for the analytic computation of any such integral. The
algorithm uses three ingredients: an operation we call general KLT, Petersen's
theorem applied to the existence of a 2-factor in any 4-regular graph and
Hamiltonian decompositions of certain 4-regular graphs. The procedure is
iterative and reduces the computation of a general integral to that of simple
building blocks. These are integrals which compute double-color-ordered partial
amplitudes in a bi-adjoint cubic scalar theory.Comment: 36+11 p
Two Results in Drawing Graphs on Surfaces
In this work we present results on crossing-critical graphs drawn on non-planar surfaces and results on edge-hamiltonicity of graphs on the Klein bottle. We first give an infinite family of graphs that are 2-crossing-critical on the projective plane. Using this result, we construct 2-crossing-critical graphs for each non-orientable surface. Next, we use 2-amalgamations to construct 2-crossing-critical graphs for each orientable surface other than the sphere. Finally, we contribute to the pursuit of characterizing 4-connected graphs that embed on the Klein bottle and fail to be edge-hamiltonian. We show that known 4-connected counterexamples to edge-hamiltonicity on the Klein bottle are hamiltonian and their structure allows restoration of edge-hamiltonicity with only a small change
Combinatorics
This is the report on the Oberwolfach workshop on Combinatorics, held 1–7 January 2006. Combinatorics is a branch of mathematics studying families of mainly, but not exclusively, finite or countable structures – discrete objects. The discrete objects considered in the workshop were graphs, set systems, discrete geometries, and matrices. The programme consisted of 15 invited lectures, 18 contributed talks, and a problem session focusing on recent developments in graph theory, coding theory, discrete geometry, extremal combinatorics, Ramsey theory, theoretical computer science, and probabilistic combinatorics
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