| Title:
|
Decomposition of complete graphs into $(0,2)$-prisms (English) |
| Author:
|
Cichacz, Sylwia |
| Author:
|
Dib, Soleh |
| Author:
|
Froncek, Dalibor |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
37-43 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
R. Frucht and J. Gallian (1988) proved that bipartite prisms of order $2n$ have an $\alpha $-labeling, thus they decompose the complete graph $K_{6nx+1}$ for any positive integer $x$. We use a technique called the $\rho ^{+}$-labeling introduced by S. I. El-Zanati, C. Vanden Eynden, and N. Punnim (2001) to show that also some other families of 3-regular bipartite graphs of order $2n$ called generalized prisms decompose the complete graph $K_{6nx+1}$ for any positive integer $x$. (English) |
| Keyword:
|
decompositions |
| Keyword:
|
prism |
| Keyword:
|
$\rho ^+$-labeling |
| MSC:
|
05B30 |
| MSC:
|
05C51 |
| MSC:
|
05C70 |
| MSC:
|
05C78 |
| idZBL:
|
Zbl 06391473 |
| idMR:
|
MR3247441 |
| DOI:
|
10.1007/s10587-014-0080-2 |
| . |
| Date available:
|
2014-09-29T09:31:11Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143946 |
| . |
| Reference:
|
[1] Cichacz, S., Froncek, D.: Factorization of $K_{n,n}$ into $(0,j)$-prisms.Inf. Process. Lett. 109 (2009), 932-934. Zbl 1197.05116, MR 2541974, 10.1016/j.ipl.2009.04.024 |
| Reference:
|
[2] Cichacz, S., Fronček, D., Kovář, P.: Note on decomposition of $K_{n,n}$ into $(0,j)$-prisms.Combinatorial Algorithms Lecture Notes in Computer Science 5874 Springer, Berlin (2009), 125-133. Zbl 1267.05203, MR 2577931, 10.1007/978-3-642-10217-2_15 |
| Reference:
|
[3] Cichacz, S., Fronček, D., Kovář, P.: Decomposition of complete bipartite graphs into generalized prisms.Eur. J. Comb. 34 (2013), 104-110. Zbl 1256.05184, MR 2974274, 10.1016/j.ejc.2012.07.018 |
| Reference:
|
[4] El-Zanati, S. I., Eynden, C. Vanden, Punnim, N.: On the cyclic decomposition of complete graphs into bipartite graphs.Australas. J. Comb. 24 (2001), 209-219. MR 1852820 |
| Reference:
|
[5] Frucht, R., Gallian, J.: Labeling prisms.Ars Comb. 26 (1988), 69-82. Zbl 0678.05053, MR 0982109 |
| Reference:
|
[6] Huang, J. H., Skiena, S.: Gracefully labeling prisms.Ars Comb. 38 (1994), 225-242. Zbl 0818.05056, MR 1310422 |
| Reference:
|
[7] Jungreis, D. S., Reid, M.: Labeling grids.Ars Comb. 34 (1992), 167-182. Zbl 0774.05087, MR 1206560 |
| Reference:
|
[8] Rosa, A.: On certain valuations of the vertices of a graph.Theory of Graphs Int. Symp. Rome 1966 (1967), 349-355. Zbl 0193.53204, MR 0223271 |
| . |
