On subgraphs of Cartesian product graphs

Klavžar, Sandi; Lipovec, Alenka; Petkovšek, Marko

doi:10.1016/s0012-365x(01)00085-1

Cited by 16 publications

(21 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Subgraphs of Cartesian product graphs were first investigated by Lamprey and Barnes [19,20] and later characterized in [18] using certain vertex-labelings. Additional results are given in [5].…”

Section: Subgraphs Of Hamming Graphsmentioning

confidence: 99%

“…The images of vertices under the quotient map are also given and finally the embedding of G into K 3 & K 3 is shown. The characterization of subgraphs of Cartesian product graphs G from [18] involves vertex-labelings, where labels can use integers between 2 and jVðGÞj À 1. Hence, the present approach seems to be more convenient which we demonstrate on the following example ([18, Corollary 3]).…”

Section: Subgraphs Of Hamming Graphsmentioning

confidence: 99%

See 1 more Smart Citation

Characterizing subgraphs of Hamming graphs

Klavžar

Peterin

2005

Journal of Graph Theory

Self Cite

View full text Add to dashboard Cite

Cartesian products of complete graphs are known as Hamming graphs. Using embeddings into Cartesian products of quotient graphs we characterize subgraphs, induced subgraphs, and isometric subgraphs of Hamming graphs. For instance, a graph G is an induced subgraph of a Hamming graph if and only if there exists a labeling of E(G) fulfilling the following two conditions: (i) edges of a triangle receive the same label; (ii) for any vertices u and v at distance at least two, there exist two labels which both appear on any induced u; v-path.

show abstract

Section: Subgraphs Of Hamming Graphsmentioning

confidence: 99%

Section: Subgraphs Of Hamming Graphsmentioning

confidence: 99%

Characterizing subgraphs of Hamming graphs

Klavžar

Peterin

2005

Journal of Graph Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…(Note that in such a coloring neighboring vertices are allowed to have the same color.) Theorem 1.1 (KlavÄ zar et al [4]). Let G be a connected graph on at least three vertices.…”

Section: Introductionmentioning

confidence: 99%

“…This could be a hard task since in [5,6] only a few examples of such graphs were presented. Recently, KlavÄ zar et al presented an inÿnite family of basic S-prime graphs as one of the main results of [4]. More importantly, they proved a characterization of S-composite graphs using a certain coloring of vertices.…”

Section: Introductionmentioning

confidence: 99%

On subgraphs of Cartesian product graphs and S-primeness

Brešar

2004

Discrete Mathematics

View full text Add to dashboard Cite

In this paper we consider S-prime graphs, that is the graphs that cannot be represented as nontrivial subgraphs of nontrivial Cartesian products of graphs. Lamprey and Barnes characterized S-prime graphs via so-called basic S-prime graphs that form a subclass of all S-prime graphs. However, the structure of basic S-prime graphs was not known very well. In this paper we prove several characterizations of basic S-prime graphs. In particular, the structural characterization of basic S-prime graphs of connectivity 2 enables us to present several inÿnite families of basic S-prime graphs. Furthermore, simple S-prime graphs are introduced that form a relatively small subclass of basic S-prime graphs, and it is shown that every basic S-prime graph can be obtained from a simple S-prime graph by a sequence of certain transformations called extensions.

show abstract

“…The opposite direction was taken in [15] where subgraphs and induced subgraphs of Cartesian products of complete graphs are characterized via quotient graphs and certain edge-labelings. Another characterization of subgraphs of Cartesian products can be found in [14] using some different methods.…”

Section: Introductionmentioning

confidence: 99%

Characterizing Flag Graphs and Induced Subgraphs of Cartesian Product Graphs

Peterin

2004

Order

View full text Add to dashboard Cite

The vertices of the flag graph (P ) of a graded poset P are its maximal chains. Two vertices are adjacent whenever two maximal chains differ in exactly one element. In this paper we characterize induced subgraphs of Cartesian product graphs and flag graphs of graded posets. The latter class of graphs lies between isometric and induced subgraphs of Cartesian products in the embedding structure theory. Both characterization use certain edge-labelings of graphs. Mathematics Subject Classifications (2000):

show abstract

On subgraphs of Cartesian product graphs

Cited by 16 publications

References 11 publications

Characterizing subgraphs of Hamming graphs

Characterizing subgraphs of Hamming graphs

On subgraphs of Cartesian product graphs and S-primeness

Characterizing Flag Graphs and Induced Subgraphs of Cartesian Product Graphs

Contact Info

Product

Resources

About