35,248 research outputs found
The structure of graphs with a vital linkage of order 2
A linkage of order k of a graph G is a subgraph with k components, each of which is a path. A linkage is vital if it spans all vertices, and no other linkage connects the same pairs of end vertices. We give a characterization of the graphs with a vital linkage of order 2: they are certain minors of a family of highly structured graphs
The structure of graphs with a vital linkage of order 2 *
Abstract A linkage of order k of a graph G is a subgraph with k components, each of which is a path. A linkage is vital if it spans all vertices, and no other linkage connects the same pairs of end vertices. We give a characterization of the graphs with a vital linkage of order 2: they are certain minors of a family of highly structured graphs
Packing Topological Minors Half-Integrally
The packing problem and the covering problem are two of the most general
questions in graph theory. The Erd\H{o}s-P\'{o}sa property characterizes the
cases when the optimal solutions of these two problems are bounded by functions
of each other. Robertson and Seymour proved that when packing and covering
-minors for any fixed graph , the planarity of is equivalent with the
Erd\H{o}s-P\'{o}sa property. Thomas conjectured that the planarity is no longer
required if the solution of the packing problem is allowed to be half-integral.
In this paper, we prove that this half-integral version of Erd\H{o}s-P\'{o}sa
property holds with respect to the topological minor containment, which easily
implies Thomas' conjecture. Indeed, we prove an even stronger statement in
which those subdivisions are rooted at any choice of prescribed subsets of
vertices. Precisely, we prove that for every graph , there exists a function
such that for every graph , every sequence of
subsets of and every integer , either there exist subgraphs
of such that every vertex of belongs to at most two
of and each is isomorphic to a subdivision of whose
branch vertex corresponding to belongs to for each , or
there exists a set with size at most intersecting all
subgraphs of isomorphic to a subdivision of whose branch vertex
corresponding to belongs to for each .
Applications of this theorem include generalizations of algorithmic
meta-theorems and structure theorems for -topological minor free (or
-minor free) graphs to graphs that do not half-integrally pack many
-topological minors (or -minors)
Plasma sprayed titanium coatings with/without a shroud
Abstract:
Titanium coatings were deposited by plasma spraying with and without a shroud. The titanium coatings were then assessed by scanning electron microscopy. A comparison in microstructure between titanium coatings with and
without the shroud was carried out. The results showed that the shroud played an important role in protecting the titanium particles from oxidation. The presence of
the shroud led to a reduction in coating porosity. The reduction in air entrainment with t he shroud resulted in better heating of the particles, and an enhanced
microstructure with lower porosity in the shrouded titanium coatings were observed compared to the air plasma sprayed counterpart
Tetrahedral curves via graphs and Alexander duality
A tetrahedral curve is a (usually nonreduced) curve in P^3 defined by an
unmixed, height two ideal generated by monomials. We characterize when these
curves are arithmetically Cohen-Macaulay by associating a graph to each curve
and, using results from combinatorial commutative algebra and Alexander
duality, relating the structure of the complementary graph to the
Cohen-Macaulay property.Comment: 15 pages; minor revisions to v. 1 to improve clarity; to appear in
JPA
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