
For a finite group
The complete directed graph of order
A bipartite graph on
We first introduce the concept of
We are interested in ordering the elements of a subset
A graph
This paper surveys recent results for flag enumeration of polytopes, Bruhat graphs, balanced digraphs, Whitney stratified spaces and quasi-graded posets.
A bipancyclic graph on
In this paper, we find all uniquely bipancyclic graphs on 30 or fewer vertices.
A balanced complete bipartite graph is a complete bipartite graph where the degrees of its vertices differ by at most 1. In a red-blue-green coloring of the edges of a graph
A Hamiltonian graph
Let
A red-blue coloring of a graph
Let
Let
For a graph
In this paper, we determine the friendly index set of certain classes of trees and introduce a few classes of fully cordial trees.
Let
Recently, the authors proposed a fundamental theorem for the decomposing of a complete bipartite graph. They applied the theorem to obtain complete results on the decomposition of a complete bipartite graph into connected subgraphs on four vertices and up to four edges. In this paper, we decompose a complete multi-bipartite graph into its subgraphs of four vertices and five edges. We show that necessary conditions are sufficient for the decompositions, with some exceptions where decompositions do not exist
The authors previously defined the Stanton-type graph
Let
A triple system is decomposable if the blocks can be partitioned into two sets, each of which is itself a triple system. It is cyclically decomposable if the resulting triple systems are themselves cyclic. In this paper, we prove that a cyclic two-fold triple system is cyclically indecomposable if and only if it is indecomposable. Moreover, we construct cyclic three-fold triple systems of order $v$ which are cyclically indecomposable but decomposable for all
The spectrum problem for decomposition of trees with up to eight edges was introduced and solved in 1978 by Huang and Rosa. Additionally, the packing problem was settled for all trees with up to six edges by Roditty. For the first time, we consider obtaining all possible leaves in a maximum tree-packing of
Let
An
A set of vertices
Let
A permutation
We use a criterion of Tripathi and Vijay to provide a new proof of this result and to establish a similar result for permutations
A
Lovász et al. showed that for
1970-2025 CP (Manitoba, Canada) unless otherwise stated.