Neighbor sum distinguishing total colorings of triangle free planar graphs
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| 008 | 210128e20150201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10114-015-4114-y |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4114-y | ||
| 245 | 0 | 0 | |a Neighbor sum distinguishing total colorings of triangle free planar graphs |h [Elektronische Daten] |c [Ji Wang, Qiao Ma, Xue Han] |
| 520 | 3 | |a A total k-coloring c of a graph G is a proper total coloring c of G using colors of the set [k] = {1, 2, ..., k}. Let f(u) denote the sum of the color on a vertex u and colors on all the edges incident to u. A k-neighbor sum distinguishing total coloring of G is a total k-coloring of G such that for each edge uv ∈ E(G), f(u) ≠ f(v). By χ″nsd(G), we denote the smallest value k in such a coloring of G. Pilśniak and Woźniak conjectured that χ″nsd(G) ≤ Δ(G)+3 for any simple graph with maximum degree Δ(G). In this paper, by using the famous Combinatorial Nullstellensatz, we prove that the conjecture holds for any triangle free planar graph with maximum degree at least 7. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Neighbor sum distinguishing total coloring |2 nationallicence | |
| 690 | 7 | |a combinatorial Nullstellensatz |2 nationallicence | |
| 690 | 7 | |a triangle free planar graph |2 nationallicence | |
| 700 | 1 | |a Wang |D Ji |u School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China |4 aut | |
| 700 | 1 | |a Ma |D Qiao |u School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China |4 aut | |
| 700 | 1 | |a Han |D Xue |u School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/2(2015-02-01), 216-224 |x 1439-8516 |q 31:2<216 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4114-y |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-4114-y |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Wang |D Ji |u School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ma |D Qiao |u School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Han |D Xue |u School of Mathematical Sciences, University of Ji'nan, 250022, Ji'nan, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/2(2015-02-01), 216-224 |x 1439-8516 |q 31:2<216 |1 2015 |2 31 |o 10114 | ||