Results 41 to 50 of about 115,985 (312)

List Star Edge-Coloring of Subcubic Graphs

Discussiones Mathematicae Graph Theory, 2018
A star edge-coloring of a graph G is a proper edge coloring such that every 2-colored connected subgraph of G is a path of length at most 3. For a graph G, let the list star chromatic index of G, ch′st(G), be the minimum k such that for any k-uniform ...
Kerdjoudj Samia, Kostochka Alexandr, Raspaud André   +2 more
doaj   +1 more source

A different short proof of Brooks' theorem

, 2013
Lov\'asz gave a short proof of Brooks' theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case. Then we show how to extend the result to (online) list coloring via the Kernel Lemma.Comment: added cute ...
Rabern, Landon
core   +2 more sources

List-Distinguishing Colorings of Graphs [PDF]

The Electronic Journal of Combinatorics, 2011
A coloring of the vertices of a graph $G$ is said to be distinguishing provided that no nontrivial automorphism of $G$ preserves all of the vertex colors. The distinguishing number of $G$, denoted $D(G)$, is the minimum number of colors in a distinguishing coloring of $G$.
Ferrara, Michael, Flesch, Breeann, Gethner, Ellen   +2 more
openaire   +2 more sources

On $t$-Common List-Colorings

The Electronic Journal of Combinatorics, 2017
In this paper, we introduce a new variation of list-colorings. For a graph $G$  and for a given nonnegative integer $t$, a $t$-common list assignment of $G$ is a mapping $L$ which assigns each vertex $v$ a set $L(v)$ of colors such that given set of $t$ colors belong to $L(v)$ for every $v\in V(G)$.
Ho‐Jin Choi, Young Soo Kwon
openalex   +3 more sources

List Edge Coloring of Planar Graphs without 6-Cycles with Two Chords

Discussiones Mathematicae Graph Theory, 2021
A graph G is edge-L-colorable if for a given edge assignment L = {L(e) : e ∈ E(G)}, there exists a proper edge-coloring φ of G such that φ(e) ∈ L(e) for all e ∈ E(G). If G is edge-L-colorable for every edge assignment L such that |L(e)| ≥ k for all e ∈ E(
Hu Linna, Sun Lei, Wu Jian-Liang
doaj   +1 more source

A Survey on Packing Colorings

Discussiones Mathematicae Graph Theory, 2020
If S = (a1, a2, . . .) is a non-decreasing sequence of positive integers, then an S-packing coloring of a graph G is a partition of V (G) into sets X1, X2, . . .
Brešar Boštjan, Ferme Jasmina, Klavžar Sandi, Rall Douglas F.   +3 more
doaj   +1 more source

Data Reduction for Graph Coloring Problems

, 2013
This paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances. We are interested in how well polynomial-time data reduction can provably shrink instances of coloring
Bart M.P. Jansen, Bodlaender, Bodlaender, Bodlaender, Bodlaender, Bodlaender, Brandstädt, Bruce, Cai, Chor, Dell, Downey, Fellows, Fellows, Fiala, Fomin, Fomin, Fortnow, Garey, Guo, Hoàng, Jansen, Knuth, Kobler, Kratochvíl, Lokshtanov, Marx, Marx, Stefan Kratsch, Tuza, Yap   +30 more
core   +1 more source

List Distinguishing Parameters of Trees [PDF]

, 2011
A coloring of the vertices of a graph G is said to be distinguishing} provided no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, D(G), is the minimum number of colors in a distinguishing coloring of G ...
Ferrara, Michael, Gethner, Ellen, Hartke, Stephen G., Stolee, Derrick, Wenger, Paul S.   +4 more
core   +1 more source

Asymptotically Good List-Colorings

Journal of Combinatorial Theory, Series A, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

On Differences Between DP-Coloring and List Coloring [PDF]

Siberian Advances in Mathematics, 2019
8 pages, 3 figures.
Bernshteyn, Anton, Kostochka, Alexandr
openaire   +2 more sources