An outerplanar graph is a planar graph which can be embedded in the plane in such a way that all of vertices lie on the outer boundary. Many semi-structured data like the NCI dataset having about 250,000 chemical compounds can be expressed by outerplanar graphs. In this paper, we consider a data mining problem of extracting structural features from semi-structured data like the NCI dataset. For...

It is shown that for every finite set of disjoint convex polygonal obstacles in the plane, with a total of n vertices, the free space around the obstacles can be partitioned into open convex cells whose dual graph (defined below) is 2-edge connected. Intuitively, every edge of the dual graph corresponds to a pair of adjacent cells that are both incident to the same vertex. Aichholzer et al. rec...

Let $G$ be a graph. Let $f:V(G)to{0,1,2, ldots, k-1}$ be a map where $k in mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $left|f(u)-f(v)right|$. $f$ is called a $k$-total difference cordial labeling of $G$ if $left|t_{df}(i)-t_{df}(j)right|leq 1$, $i,j in {0,1,2, ldots, k-1}$ where $t_{df}(x)$ denotes the total number of vertices and the edges labeled with $x$.A graph with admits a...

Abstract We review work by Campana–Oguiso–Peternell (J Differ Geom 85(3):397–424, 2010) and Verbitsky (Geom Funct Anal 19(5):1481–1493, showing that a semi-positive line bundle on hyperkähler manifold admits at least one non-trivial section. This is modest but tangible evidence towards the SYZ conjecture for manifolds.

Graph-based semi-supervised learning methods are based on some smoothness assumption about the data. As a discrete approximation of the data manifold, the graph plays a crucial role in the success of such graphbased methods. In most existing methods, graph construction makes use of a predefined weighting function without utilizing label information even when it is available. In this work, by in...

A graph is supereulerian if it has a spanning eulerian subgraph. There is a reduction method to determine whether a graph is supereulerian, and it can also be applied to study other concepts, e.g., hamiltonian line graphs, a certain type of double cycle cover, and the total interval number of a graph. We outline the research on supereulerian graphs, the reduction method and its applications.