Vertex partitions of (C_3,C_4,C_6)-free planar graphs

by   Francois Dross, et al.

A graph is (k_1,k_2)-colorable if its vertex set can be partitioned into a graph with maximum degree at most k_1 and and a graph with maximum degree at most k_2. We show that every (C_3,C_4,C_6)-free planar graph is (0,6)-colorable. We also show that deciding whether a (C_3,C_4,C_6)-free planar graph is (0,3)-colorable is NP-complete.


page 1

page 2

page 3

page 4


The complexity of the Bondage problem in planar graphs

A set S⊆ V(G) of a graph G is a dominating set if each vertex has a neig...

Complexity of planar signed graph homomorphisms to cycles

We study homomorphism problems of signed graphs. A signed graph is an un...

Partitioning edges of a planar graph into linear forests and a matching

We show that the edges of any planar graph of maximum degree at most 9 c...

Partitioning sparse graphs into an independent set and a graph with bounded size components

We study the problem of partitioning the vertex set of a given graph so ...

A Note on Plus-Contacts, Rectangular Duals, and Box-Orthogonal Drawings

A plus-contact representation of a planar graph G is called c-balanced i...

Halin graphs are 3-vertex-colorable except even wheels

A Halin graph is a graph obtained by embedding a tree having no nodes of...

Please sign up or login with your details

Forgot password? Click here to reset