Martin Tancer

Injective colorings of planar graphs with few colors

An injective coloring of a graph is a vertex coloring where two vertices have distinct colors if a path of length two exists between them. In this paper some results on injective colorings of planar graphs with few colors are presented. We show that all planar graphs of girth >= 19 and maximum degree @D are injectively @D-colorable. We also show that all planar graphs of girth >= 10 are injectively (@D+1)-colorable, that @D+4 colors are sufficient for planar graphs of girth >= 5 if @D is large enough, and that subcubic planar graphs of girth >= 7 are injectively 5-colorable.

List-Coloring Squares of Sparse Subcubic Graphs

The problem of coloring the square of a graph naturally arises in connection with the distance labelings, which have been studied intensively. We consider this problem for sparse subcubic graphs. We show that the choosability

Recognition of Collapsible Complexes is NP-Complete

\chi_\ell(G^2)

Embeddability in the 3-sphere is decidable

of the square of a subcubic graph

A Geometric Proof of the Colored Tverberg Theorem

G

Intersection Patterns of Convex Sets via Simplicial Complexes: A Survey

of maximum average degree

Backbone colorings of graphs with bounded degree

d

Backbone Colorings and Generalized Mycielski Graphs

is at most four if

Construction of Large Graphs with No Optimal Surjective L (2,1)-Labelings

d<24/11

Bounds for Pach's Selection Theorem and for the Minimum Solid Angle in a Simplex

and