PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 34 | 4 | 769-799
Tytuł artykułu

The 1 , 2 , 3-Conjecture And 1 , 2-Conjecture For Sparse Graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct. The 1, 2-Conjecture states that if vertices also receive labels and the vertex label is added to the sum of its incident edge labels, then adjacent vertices can be distinguished using only {1, 2}. We show that various configurations cannot occur in minimal counterexamples to these conjectures. Discharging then confirms the conjectures for graphs with maximum average degree less than 8/3. The conjectures are already confirmed for larger families, but the structure theorems and reducibility results are of independent interest.
Słowa kluczowe
Wydawca
Rocznik
Tom
34
Numer
4
Strony
769-799
Opis fizyczny
Daty
wydano
2014-11-01
otrzymano
2013-03-29
poprawiono
2013-11-13
zaakceptowano
2013-11-13
online
2014-11-15
Twórcy
  • Zhejiang Normal University, Jinhua, China and University of Illinois, Urbana, IL, USA, west@math.uiuc.edu
Bibliografia
  • [1] L. Addario-Berry, K. Dalal, C. McDiarmid, B.A. Reed and A. Thomason, Vertex- colouring edge-weightings, Combinatorica 27 (2007) 1-12. doi:10.1007/s00493-007-0041-6
  • [2] L. Addario-Berry, K. Dalal and B.A. Reed, Degree constrained subgraphs, Discrete Appl. Math. 156 (2008) 1168-1174. doi:10.1016/j.dam.2007.05.059
  • [3] N. Alon, Combinatorial Nullstellensatz , Combin. Probab. Comput. 8 (1999) 7-29. doi:10.1017/S0963548398003411
  • [4] T. Bartnicki, J. Grytczuk and S. Niwczyk, Weight choosability of graphs, J. Graph Theory 60 (2009) 242-256. doi:10.1002/jgt.20354
  • [5] M. Kalkowski, A note on the 1, 2-conjecture, submitted (also in Ph.D. Thesis, 2009).
  • [6] M. Kalkowski, M. Karónski and F. Pfender, Vertex-coloring edge-weightings: towards the 1-2-3-conjecture, J. Combin. Theory (B) 100 (2010) 347-349. doi:10.1016/j.jctb.2009.06.002
  • [7] M. Karónski, T. Luczak and A. Thomason, Edge weights and vertex colours, J. Combin. Theory (B) 91 (2004) 151-157. doi:10.1016/j.jctb.2003.12.001
  • [8] J. Przyby lo and M. Wózniak, On a 1, 2 conjecture, Discrete Math. Theoret. Comput. Sci. 12 (2010) 101-108.
  • [9] B. Seamone, The 1-2-3 conjecture and related problems: a survey, submitted (http://arxiv.org/abs/1211.5122).
  • [10] T. Wang and Q. Yu, On vertex-coloring 13-edge-weighting, Front. Math. China 3 (2008) 581-587. doi:10.1007/s11464-008-0041-x
  • [11] T.-L. Wong, X. Zhu and D. Yang, List total weighting of graphs, in: G.O.H. Katona, A. Schrijver, T. Szőnyi and G. Sági, Eds., Fete of Combinatorics and Computer Science, Bolyai Soc. Math. Stud., vol. 20 (Springer, Berlin, Heidelberg, 2010) 337-353. doi:10.1007/978-3-642-13580-4 13
  • [12] T.-L. Wong and X. Zhu, Total weight choosability of graphs, J. Graph Theory 66 (2011) 198-212. doi:10.1002/jgt.20500
  • [13] T.-L. Wong and X. Zhu, Every graph is (2, 3)-choosable, submitted.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1768
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.