46,601 research outputs found
Probabilistic learning on graphs via contextual architectures
We propose a novel methodology for representation learning on graph-structured data, in which a stack of Bayesian Networks learns different distributions of a vertex's neighbour- hood. Through an incremental construction policy and layer-wise training, we can build deeper architectures with respect to typical graph convolutional neural networks, with benefits in terms of context spreading between vertices. First, the model learns from graphs via maximum likelihood estimation without using target labels. Then, a supervised readout is applied to the learned graph embeddings to deal with graph classification and vertex classification tasks, showing competitive results against neural models for graphs. The computational complexity is linear in the number of edges, facilitating learning on large scale data sets. By studying how depth affects the performances of our model, we discover that a broader context generally improves performances. In turn, this leads to a critical analysis of some benchmarks used in literature
On Murty-Simon Conjecture II
A graph is diameter two edge-critical if its diameter is two and the deletion
of any edge increases the diameter. Murty and Simon conjectured that the number
of edges in a diameter two edge-critical graph on vertices is at most
and the extremal graph is the complete
bipartite graph .
In the series papers [7-9], the Murty-Simon Conjecture stated by Haynes et al.
is not the original conjecture, indeed, it is only for the diameter two
edge-critical graphs of even order. In this paper, we completely prove the
Murty-Simon Conjecture for the graphs whose complements have vertex
connectivity , where ; and for the graphs whose
complements have an independent vertex cut of cardinality at least three.Comment: 9 pages, submitted for publication on May 10, 201
On building 4-critical plane and projective plane multiwheels from odd wheels
We build unbounded classes of plane and projective plane multiwheels that are
4-critical that are received summing odd wheels as edge sums modulo two. These
classes can be considered as ascending from single common graph that can be
received as edge sum modulo two of the octahedron graph O and the minimal wheel
W3. All graphs of these classes belong to 2n-2-edges-class of graphs, among
which are those that quadrangulate projective plane, i.e., graphs from
Gr\"otzsch class, received applying Mycielski's Construction to odd cycle.Comment: 10 page
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