
Let
where
In an edge-colored graph, a cycle is said to be alternating, if the successive edges in it differ in color. In this work, we consider the problem of finding alternating cycles through
It is shown that the obvious necessary condition for the existence of a
We prove that for any tree
We construct new simple
An
We propose several invariants for cycle systems and
Let
We give the numbers of nonisomorphic
A union-closed family
The concept of the star chromatic number of a graph was introduced by Vince
We obtain a formula for the number of finite lattices of a given height and cardinality that have a series-parallel and interval order. Our approach is to consider a naturally defined class of
It is known that if there are base sequences of lengths
As a network begins losing links or nodes, eventually there is a loss in its effectiveness. Thus, communication networks must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible reconstruction of the network. Many graph theoretical parameters have been used to describe the stability of communication networks, including connectivity, integrity, toughness, tenacity, and binding number. Several of these deal with two fundamental questions about the resulting graph. How many vertices can still communicate? How difficult is it to reconnect the graph? For any fixed integers
In this note, we study a group operation on the set of all row-Latin squares of order
Three general constructions for covers are given. A cover is a set of
In a complete bipartite graph
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