TITLE

# Uniformly Resolvable Cycle Decompositions with Four Different Factors

AUTHOR(S)
Odabaşı, Uğur; Özkan, Sibel
PUB. DATE
November 2017
SOURCE
Graphs & Combinatorics;Nov2017, Vol. 33 Issue 6, p1591
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
In this paper, we consider uniformly resolvable decompositions of complete graph $$K_v$$ (or $$K_v$$ minus a 1-factor I for even v) into cycles. We will focus on the existence of factorizations of $$K_v$$ or $$K_v-I$$ containing up to four non-isomorphic factors. We obtain all possible solutions for uniform factors involving 4, m, 2 m and 4 m-cycles with a few possible exceptions when m is odd.
ACCESSION #
126308048

## Related Articles

• On the Biclique Cover of the Complete Graph. Moazami, Farokhlagha; Soltankhah, Nasrin // Graphs & Combinatorics;Nov2015, Vol. 31 Issue 6, p2347

Let $$K$$ be a set of $$k$$ positive integers. A biclique cover of type $$K$$ of a graph $$G$$ is a collection of complete bipartite subgraphs of $$G$$ such that for every edge $$e$$ of $$G$$ , the number of bicliques need to cover $$e$$ is a member of $$K$$ . If $$K=\{1,2,\ldots , k\}$$ then...

• Vertex-Disjoint Cycles of Order Eight with Chords in a Bipartite Graph. QINGSONG ZOU; HONGYU CHEN; GUOJUN LI // Bulletin of the Malaysian Mathematical Sciences Society;2013, Vol. 36 Issue 1, p255

Let G = (V1,V2;E) be a bipartite graph with âˆ£ V1 âˆ£=âˆ£ V2 âˆ£= 4k, where k is a positive integer. In this paper, it is proved that if the minimum degree of G is at least 3k+1, then G contains k vertex-disjoint cycles of order eight such that each of them has at least two chords.

• Radio Mean Number of Certain Graphs. Ponraj, R.; Narayanan, S. Sathish // International Journal of Mathematical Combinatorics;2016, Vol. 2, p51

A radio mean labeling of a connected graph G is a one to one map f from the vertex set V (G) to the set of natural numbers N such that for each distinct vertices u and v of G, d (u, v) + [ f(u)+f(v)/2]l≥ 1 + diam (G). The radio mean number of f, rmn (f), is the maximum number assigned to...

• BOUNDS ON THE GLOBAL OFFENSIVE k-ALLIANCE NUMBER IN GRAPHS. Chellali, Mustapha; Haynes, Teresa W.; Randerath, Bert; Volkmann, Lutz // Discussiones Mathematicae: Graph Theory;2009, Vol. 29 Issue 3, p597

Let G = (V (G);E(G)) be a graph, and let k = 1 be an integer. A set S = V (G) is called a global offensive k-alliance if |N(v) n S| = |N(v)-S|+k for every v ? V (G)-S, where N(v) is the neighborhood of v. The global offensive k-alliance number ?ko (G) is the minimum cardinality of a global...

• Edge-disjoint Open Trails in Complete Bipartite Multigraphs. Cichacz, Sylwia; G�rlich, Agnieszka // Graphs & Combinatorics;Mar2010, Vol. 26 Issue 2, p207

Let r Ka,b be a complete bipartite multigraph. We show a necessary and sufficient condition for a multigraph r Ka,b to be arbitrarily decomposable into open trails. We extend the results obtained by Balister for complete graphs (Balister in Probab Comput 10:463-499, 2001). Moreover we show that...

• On the Decomposition of Graphs into Complete Bipartite Graphs. Jinquan Dong; Yanpei Liu // Graphs & Combinatorics;Sep2007, Vol. 23 Issue 3, p255

In a complete bipartite decomposition Ï€ of a graph, we consider the number Ï‘( v;Ï€) of complete bipartite subgraphs incident with a vertex v. Let Ï‘( G)= $$\min \limits_{\pi } \max \limits_{v\in V(G)}$$ Ï‘( v;Ï€). In this paper the exact values of Ï‘( G) for complete...

• Acyclic Coloring of Central Graphs. Arundhadhi, R.; Sattanathan, R. // International Journal of Computer Applications;Jan2012, Vol. 38, p55

The purpose of this study is to discuss the acyclic coloring and acyclic chromatic number of central graph of cycles(Cn),complete bipartite graphs(Km,n) and complete graphs(Kn),denoted respectively by C(Cn),C(Km,n) and C(Kn).

• Mining Suggestions for Recommender Systems. Nasreen, B.; Safiya Parvin, A. // International Journal of Computer Science & Information Technolo;2014, Vol. 5 Issue 1, p459

Recommender systems are systems that suggest items to the users of the web to help them find most relevant items of interest. These recommended items could include a movie, an image, query suggestions, tag recommendation etc. Data sources are modelled as graphs and are subjected to a naive...

• Maximizing the Total Resolution of Graphs. Argyriou, E.N.; Bekos, M.A.; Symvonis, A. // Computer Journal;Jul2013, Vol. 56 Issue 7, p887

A major factor affecting the readability of a graph drawing is its resolution. In the graph drawing literature, the resolution of a drawing is either measured based on the angles formed by consecutive edges incident on a common vertex (angular resolution) or by the angles formed at edge...

• Total Domination Edge Critical Graphs with Total Domination Number Three and Many Dominating Pairs. Balbuena, Camino; Hansberg, Adriana; Haynes, Teresa; Henning, Michael // Graphs & Combinatorics;Sep2015, Vol. 31 Issue 5, p1163

A graph $$G$$ is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph $$G$$ of order $$n$$ is at most $$\lfloor n^2/4 \rfloor$$ and that the extremal graphs are the...

Share