Induced Acyclic Path Decomposition in Graphs
نویسنده
چکیده
A decomposition of a graph G is a collection ψ of graphs H1, H2, . . . , Hr of G such that every edge of G belongs to exactly one Hi. If each Hi is either an induced path in G, then ψ is called an induced acyclic path decomposition of G and if each Hi is a (induced) cycle in G then ψ is called a (induced) cycle decomposition of G. The minimum cardinality of an induced acyclic path decomposition of G is called the induced acyclic path decomposition number of G and is denoted by πia(G). Similarly the cyclic decomposition number πc(G) is defined. In this paper we begin an investigation of these parameters. Keywords—Cycle decomposition, Induced acyclic path decomposition, Induced acyclic path decomposition number.
منابع مشابه
Induced label graphoidal graphs
Let G be a non-trivial, simple, finite, connected and undirected graph of order n and size m. An induced acyclic graphoidal decomposition (IAGD) of G is a collection ψ of non-trivial and internally disjoint induced paths in G such that each edge of G lies in exactly one path of ψ. For a labeling f : V → {1, 2, 3, . . . , n}, let ↑ Gf be the directed graph obtained by orienting the edges uv of G...
متن کاملOn Acyclic Vertex Coloring of Grid like graphs
d-dimensional partial tori are graphs that can be expressed as cartesian product of d graphs each of which is an induced path or cycle. Some well known graphs like d-dimensional hypercubes, meshes and tori are examples belong to this class. Muthu et al.[MNS06] have studied the problem of acyclic edge coloring for such graphs. We try to explore the acyclic vertex coloring problem for these graph...
متن کاملInduced Acyclic Graphoidal Covers in a Graph
An induced acyclic graphoidal cover of a graph G is a collection ψ of open paths in G such that every path in ψ has atleast two vertices, every vertex of G is an internal vertex of at most one path in ψ, every edge of G is in exactly one path in ψ and every member of ψ is an induced path. The minimum cardinality of an induced acyclic graphoidal cover of G is called the induced acyclic graphoida...
متن کاملOn Compact and Efficient Routing in Certain Graph Classes (Extended Abstract)
In this paper we refine the notion of tree-decomposition by introducing acyclic (R,D)-clustering, where clusters are subsets of vertices of a graph and R and D are the maximum radius and the maximum diameter of these subsets. We design a routing scheme for graphs admitting induced acyclic (R,D)-clustering where the induced radius and the induced diameter of each cluster are at most 2. We show t...
متن کاملOn Compact and Efficient Routing in Certain Graph Classes
In this paper we refine the notion of tree-decomposition by introducing acyclic (R,D)-clustering, where clusters are subsets of vertices of a graph and R and D are the maximum radius and the maximum diameter of these subsets. We design a routing scheme for graphs admitting induced acyclic (R,D)-clustering where the induced radius and the induced diameter of each cluster are at most 2. We show t...
متن کامل