On (p, 1)-total labelling of 1-planar graphs

Xin Zhang; Yong Yu; Guizhen Liu

Open Mathematics (2011)

  • Volume: 9, Issue: 6, page 1424-1434
  • ISSN: 2391-5455

Abstract

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A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.

How to cite

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Xin Zhang, Yong Yu, and Guizhen Liu. "On (p, 1)-total labelling of 1-planar graphs." Open Mathematics 9.6 (2011): 1424-1434. <http://eudml.org/doc/269282>.

@article{XinZhang2011,
abstract = {A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.},
author = {Xin Zhang, Yong Yu, Guizhen Liu},
journal = {Open Mathematics},
keywords = {1-planar graph; Alternating subgraph; Master; Total labelling; Discharging; frequency assignment},
language = {eng},
number = {6},
pages = {1424-1434},
title = {On (p, 1)-total labelling of 1-planar graphs},
url = {http://eudml.org/doc/269282},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Xin Zhang
AU - Yong Yu
AU - Guizhen Liu
TI - On (p, 1)-total labelling of 1-planar graphs
JO - Open Mathematics
PY - 2011
VL - 9
IS - 6
SP - 1424
EP - 1434
AB - A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.
LA - eng
KW - 1-planar graph; Alternating subgraph; Master; Total labelling; Discharging; frequency assignment
UR - http://eudml.org/doc/269282
ER -

References

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