2-distance (Δ+2)-coloring of sparse graphs

09/24/2021
by   Hoang La, et al.
0

A 2-distance k-coloring of a graph is a proper k-coloring of the vertices where vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance (Δ+2)-coloring for graphs with maximum average degree less than 8/3 (resp. 14/5) and maximum degree Δ≥ 6 (resp. Δ≥ 10). As a corollary, every planar graph with girth at least 8 (resp. 7) and maximum degree Δ≥ 6 (resp. Δ≥ 10) admits a 2-distance (Δ+2)-coloring.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/22/2021

2-distance (Δ+1)-coloring of sparse graphs using the potential method

A 2-distance k-coloring of a graph is a proper k-coloring of the vertice...
research
05/04/2021

2-distance list (Δ+ 3)-coloring of sparse graphs

A 2-distance list k-coloring of a graph is a proper coloring of the vert...
research
06/07/2021

2-distance 4-coloring of planar subcubic graphs with girth at least 21

A 2-distance k-coloring of a graph is a proper vertex k-coloring where v...
research
08/28/2022

Revisiting Semistrong Edge-Coloring of Graphs

A matching M in a graph G is semistrong if every edge of M has an endver...
research
05/20/2020

Improved bounds for some facially constrained colorings

A facial-parity edge-coloring of a 2-edge-connected plane graph is a fac...
research
07/21/2020

Breaking the 2^n barrier for 5-coloring and 6-coloring

The coloring problem (i.e., computing the chromatic number of a graph) c...
research
08/22/2020

Parameter Estimation for Undirected Graphical Models with Hard Constraints

The hardcore model on a graph G with parameter λ>0 is a probability meas...

Please sign up or login with your details

Forgot password? Click here to reset