Related papers: Graph Search Trees and Their Leaves
We consider the design of adaptive data structures for searching elements of a tree-structured space. We use a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of…
Graphs and their traversal is becoming significant as it is applicable to various areas of mathematics, science and technology. Various problems in fields as varied as biochemistry (genomics), electrical engineering (communication…
A typical example that behaves computationally different in subclasses of chordal graphs is the \textsc{Subset Feedback Vertex Set} (SFVS) problem: given a vertex-weighted graph $G=(V,E)$ and a set $S\subseteq V$, the \textsc{Subset…
Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…
We introduce a model for the retrieval of information hidden in legal texts. These are typically organised in a hierarchical (tree) structure, which a reader interested in a given provision needs to explore down to the "deepest" level…
A branch vertex in a tree is a vertex of degree at least three. We prove that, for all $s\geq 1$, every connected graph on $n$ vertices with minimum degree at least $(\frac{1}{s+3}+o(1))n$ contains a spanning tree having at most $s$ branch…
We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
Graceful tree conjecture is a well-known open problem in graph theory. Here we present a computational approach to this conjecture. An algorithm for finding graceful labelling for trees is proposed. With this algorithm, we show that every…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Search engines play a vital role in day to day life on internet. People use search engines to find content on internet. Cloud computing is the computing concept in which data is stored and accessed with the help of a third party server…
The \emph{linear vertex arboricity} of a graph is the smallest number of sets into which the vertices of a graph can be partitioned so that each of these sets induces a linear forest. Chaplick et al. [JoCG 2020] showed that, somewhat…
A vertex of degree one is called an end-vertex, and an end-vertex of a tree is called a leaf. A tree with at most $k$ leaves is called a $k$-ended tree. For a positive integer $k$, let $t_k$ be the order of a largest $k$-ended tree. Let…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
For intractable problems on graphs of bounded treewidth, two graph parameters treedepth and vertex cover number have been used to obtain fine-grained complexity results. Although the studies in this direction are successful, we still need a…
In this paper we consider the problem of connected edge searching of weighted trees. It is shown that there exists a polynomial-time algorithm for finding optimal connected search strategy for bounded degree trees with arbitrary weights on…
Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by…
This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph…
A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number…