A multivariate Lagrange inversion formula for asymptotic calculations.
A New Approach to the Dynamic Maintenance of Maximal Points in a Plane.
A new spectral method for determining the number of spanning trees.
A note on embedding hypertrees.
A note on major sequences and external activity in trees.
A note on minimum rank and maximum nullity of sign patterns.
A note on naturally embedded ternary trees.
A note on random minimum length spanning trees.
A note on reconstructing of finite trees from small subtrees
A note on the cubical dimension of new classes of binary trees
The cubical dimension of a graph is the smallest dimension of a hypercube into which is embeddable as a subgraph. The conjecture of Havel (1984) claims that the cubical dimension of every balanced binary tree with vertices, , is . The 2-rooted complete binary tree of depth is obtained from two copies of the complete binary tree of depth by adding an edge linking their respective roots. In this paper, we determine the cubical dimension of trees obtained by subdividing twice a 2-rooted...
A note on the independent domination number versus the domination number in bipartite graphs
Let and be the domination number and the independent domination number of , respectively. Rad and Volkmann posted a conjecture that for any graph , where is its maximum degree (see N. J. Rad, L. Volkmann (2013)). In this work, we verify the conjecture for bipartite graphs. Several graph classes attaining the extremal bound and graphs containing odd cycles with the ratio larger than are provided as well.
A parametric analysis of the largest induced tree problem in random graphs
A partition of connected graphs.
A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree.
A refinement of the formula for -ary trees and the Gould-Vandermonde's convolution.
A remark on branch weights in countable trees
Let be a tree, let be its vertex. The branch weight of is the maximum number of vertices of a branch of at . The set of vertices of in which attains its minimum is the branch weight centroid of . For finite trees the present author proved that coincides with the median of , therefore it consists of one vertex or of two adjacent vertices. In this paper we show that for infinite countable trees the situation is quite different.
A reminiscence about shortest spanning subtrees
A simple bijection between binary trees and colored ternary trees.
A simple method for constructing small cubic graphs of girths 14, 15, and 16.
A tree as a finite nonempty set with a binary operation
A (finite) acyclic connected graph is called a tree. Let be a finite nonempty set, and let be the set of all trees with the property that is the vertex set of . We will find a one-to-one correspondence between and the set of all binary operations on which satisfy a certain set of three axioms (stated in this note).