| Title:
|
Combinatorial spectra using polynomials (English) |
| Author:
|
Cichacz, Sylwia |
| Author:
|
Dzúrik, Martin |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2025 |
| Pages:
|
151-165 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we would like to introduce some new methods for studying magic type-colorings of graphs or domination of graphs, based on the combinatorial spectrum on polynomial rings. We hope that this concept will be potentially useful for the graph theorists. (English) |
| Keyword:
|
Hamiltonian spectra |
| Keyword:
|
combinatorial spectra |
| Keyword:
|
domination |
| Keyword:
|
1-2-3 labeling |
| Keyword:
|
antimagic |
| Keyword:
|
graph |
| Keyword:
|
graph theory |
| Keyword:
|
coloring |
| MSC:
|
05C12 |
| MSC:
|
05C15 |
| MSC:
|
05C25 |
| MSC:
|
05C40 |
| DOI:
|
10.5817/AM2025-4-151 |
| . |
| Date available:
|
2025-12-19T13:54:38Z |
| Last updated:
|
2025-12-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153202 |
| . |
| Reference:
|
[1] Addario-Berry, L., Dalal, K., McDiarmid, C., Reed, B.A., Thomason, A.: Vertex-colouring edge-weightings.Combinatorica 27 (2007), 1–12. 10.1007/s00493-007-0041-6 |
| Reference:
|
[2] Addario-Berry, L., Dalal, K., Reed, B.A.: Degree constrainted subgraphs.Discrete Appl. Math. 156 (2008), 1168–1174. 10.1016/j.dam.2007.05.059 |
| Reference:
|
[3] Aigner, M., Triesch, E.: Irregular assignments of trees and forests.SIAM J. Discrete Math. 3 (1990), no. 4, 439–449. 10.1137/0403038 |
| Reference:
|
[4] Alon, N.: Combinatorial nullstellensatz.Combin. Probab. Comput. 8 (1999), 7–29. 10.1017/S0963548398003411 |
| Reference:
|
[5] Alon, N., Kaplan, G., Lev, A., Roditty, Y., Yuster, R.: Dence graphs are antimagic.J. Graph Theory 47 (2004), 297–309. 10.1002/jgt.20027 |
| Reference:
|
[6] Amar, D., Togni, O.: Irregularity strength of trees.Discrete Math. 190 (1998), no. 1, 15–38. 10.1016/S0012-365X(98)00112-5 |
| Reference:
|
[7] Chartrand, G., Jacobson, M.S., Lehel, J., Oellermann, O.R., Ruiz, S., Saba, F.: Irregular networks.Congr. Numer. 64 (1988), 187–192. |
| Reference:
|
[8] Chartrand, G., Thomas, T., Zhang, P.: A New Look at Hamiltonian Walks.Bull. Inst. Combin. Appl. 42 (2004), 37–52. |
| Reference:
|
[9] Dzúrik, M.: An upper bound of a generalized upper Hamiltonian number of a graph.Arch. Math. (Brno) 57 (2021), 299–311. 10.5817/AM2021-5-299 |
| Reference:
|
[10] Dzúrik, M.: Combinatorial spectra of graphs.arXiv preprint arXiv:2311.11682 (2023). |
| Reference:
|
[11] Goodman, S.E., Hedetniemi, S.T.: On Hamiltonian walks in graphs.SIAM J. Comput. 3 (1974), 214–221. Zbl 0269.05113, 10.1137/0203017 |
| Reference:
|
[12] Kalkowski, M., Karoński, M., Pfender, F.: Vertex-coloring edge-weightings: Towards the 1-2-3-conjecture. |
| Reference:
|
[13] Kalkowski, M., Karoński, M., Pfender, F.: A new upper bound for the irregularity strength of graphs.SIAM J. Discrete Math. 25 (2011), no. 3, 1319–1321. 10.1137/090774112 |
| Reference:
|
[14] Karoński, M., Łuczak, T., Thomason, A.: Edge weights and vertex colours.J. Combin. Theory Ser. B 91 (2004), 151–157. 10.1016/j.jctb.2003.12.001 |
| Reference:
|
[15] Keusch, R.: Vertex-Coloring Graphs with 4-Edge-Weightings.Combinatorica 43 (2023), 651–658. 10.1007/s00493-023-00027-6 |
| Reference:
|
[16] Keusch, R.: A solution to the 1-2-3 conjecture.J. Combin. Theory Ser. B 166 (2024), 183–202. 10.1016/j.jctb.2024.01.002 |
| Reference:
|
[17] ReVelle, C.S.: Can you protect the Roman Empire?.Johns Hopkins Magazine 49 (1997), 40. |
| Reference:
|
[18] Ringel, G., Hartsfield, N.: Pearls in Graph Theory.Academic Press, 1994. |
| Reference:
|
[19] Roushini Leely Pushpam, P., Malini Mai, T.N.M.: Edge Roman domination in graphs.J. Combin. Math. Combin. Comput. 69 (2009), 175–182. |
| Reference:
|
[20] Wang, T., Yu, Q.: On vertex-coloring 13-edge-weighting.Front. Math. China 3 (2008), 581–587. 10.1007/s11464-008-0041-x |
| Reference:
|
[21] Zhu, Xuding, Balakrishnan, R.: Combinatorial Nullstellensatz With Applications to Graph Colouring.Taylor and Francis, 2022. |
| . |
