Given a 3-colorable graph X , the 3-coloring complex B ( ) is whose vertices are all independent sets which occur as color classes in some of . Two C D ∈ V joined by an edge if and appear together The 3-colorable. Graphs for isomorphic to termed reflexive graphs. In this paper, we consider 3-edge-colorings cubic graphs allow half-edges. Then complexes their line main result paper surprising out...

Based on the notions of locality and recognizability for n-dimensional languages ndimensionally colorable 1-dimensional languages are introduced. It is shown: A language L is in NP if and only if L is n-dimensionally colorable for some n. An analogous characterization in terms of deterministic n-dimensional colorability is obtained for P. The addition of one unbounded dimension for coloring lea...

A graph is (7, 2)-edge-choosable if, for every assignment of lists of size 7 to the edges, it is possible to choose two colors for each edge from its list so that no color is chosen for two incident edges. We show that every 3-edge-colorable graph is (7, 2)-edge-choosable and also that many non-3-edge-colorable 3-regular graphs are (7, 2)-edge-choosable.

A graph G with a list of colors L(v) and weight w(v) for each vertex v is (L,w)-colorable if one can choose a subset of w(v) colors from L(v) for each vertex v, such that adjacent vertices receive disjoint color sets. In this paper, we give necessary and sufficient conditions for a weighted path to be (L,w)-colorable for some list assignments L. Furthermore, we solve the problem of the free-cho...

A graph is (7, 2)-edge-choosable if, for every assignment of lists of size 7 to the edges, it is possible to choose two colors for each edge from its list so that no color is chosen for two incident edges. We show that every 3-edge-colorable graph is (7, 2)-edge-choosable and also that many non-3-edge-colorable 3-regular graphs are (7, 2)-edge-choosable.

It was proved in [Z. Dvořàk, D. Kràl, P. Nejedlỳ, R. Škrekovski, Coloring squares of planar graphs with girth six, European J. Combin. 29 (4) (2008) 838–849] that every planar graph with girth g ≥ 6 and maximum degree ∆ ≥ 8821 is 2-distance (∆ + 2)-colorable. We prove that every planar graph with g ≥ 6 and∆ ≥ 18 is 2-distance (∆+ 2)-colorable. © 2009 Elsevier B.V. All rights reserved.

A (c1, c2, ..., ck)-coloring of G is a mapping φ : V (G) 7→ {1, 2, ..., k} such that for every i, 1 ≤ i ≤ k, G[Vi] has maximum degree at most ci, where G[Vi] denotes the subgraph induced by the vertices colored i. Borodin and Raspaud conjecture that every planar graph without intersecting triangles and 5-cycles is 3-colorable. We prove in this paper that every planar graph without intersecting ...

A graph is (7, 2)-edge-choosable if, for every assignment of lists of size 7 to the edges, it is possible to choose two colors for each edge from its list so that no color is chosen for two incident edges. We show that every 3-edge-colorable graph is (7, 2)-edge-choosable and also that many non-3-edge-colorable 3-regular graphs are (7, 2)-edge-choosable.

L coloring is an important generalization of ordinary graph coloring, introduced independently by Vizing [6] and Erdős, Rubin, and Taylor [4]. It is defined as follows. Let G be a graph and suppose that for each vertex v ∈ V (G), a set of available colors L(v), called the list of v, is specified. A proper coloring c of G is an L-coloring if c(v) ∈ L(v) for all v ∈ V (G). G is said to be L-color...