Frontiers of Mathematics in China >
Injective coloring of planar graphs with girth 5
Published date: 15 Jun 2022
Copyright
A coloring of a graph is injective if its restriction to the neighbour of any vertex is injective. The injective chromatic number of a graph is the least such that there is an injective -coloring. In this paper, we prove that for each planar graph with and , .
Key words: Planar graph; girth; injective coloring; face
Yuehua BU , Piaopiao YE . Injective coloring of planar graphs with girth 5[J]. Frontiers of Mathematics in China, 2022 , 17(3) : 473 -484 . DOI: 10.1007/s11464-022-1018-x
1 |
Bu Y H, Chen D, Raspaud A, Wang W. Injective coloring of planar graphs. Discrete Appl. Math., 2009, 157(4): 663–672
|
2 |
Bu Y H, Lu K. List injective coloring of planar graphs with girth 5, 6, 8. Discrete Appl. Math., 2013, 161(10/11): 1367–1377
|
3 |
Cranston D, Kim S, Yu G X. Injective colorings of graphs with low average degree. Algorithmica, 2010, 60(3): 553–568
|
4 |
Cranston D, Kim S, Yu G X. Injective colorings of sparse graphs. Discrete Math., 2010, 310(21): 2965–2973
|
5 |
Dong W, Lin W S. Injective coloring of planar graphs with girths 6. Discrete Math., 2013, 313(12): 1302–1311
|
6 |
Dong W, Lin W S. Injective coloring of planar graphs with girths 5. Discrete Math., 2014, 315/316(12): 120–127
|
7 |
Doyon A, Hahn G, Raspaud A. Some bounds on the injective chromatic number of graphs. Discrete Math., 2012, 310(6): 585–590
|
8 |
Hahn G, Kratochvíl J, Širáň J, Sotteau D. On the injective chromatic number of graphs. Discrete Math., 2002, 256(1/2): 179–192
|
9 |
Li R, Xu B G. Injective choosability of planar graphs of girth five and six. Discrete Math., 2012, 312(9): 1260–1265
|
10 |
Lužar B, Škrekovski S, Tancer M. Injective colorings of planar graphs with few colors. Discrete Math., 2009, 309(18): 5636–5649
|
/
〈 | 〉 |