Every toroidal graph without adjacent triangles is (4, 1)*-choosable
نویسندگان
چکیده
In this paper, a structural theorem about toroidal graphs is given that strengthens a result of Borodin on plane graphs. As a consequence, it is proved that every toroidal graph without adjacent triangles is (4, 1)∗-choosable. This result is best possible in the sense that K7 is a non-(3, 1)∗-choosable toroidal graph. A linear time algorithm for producing such a coloring is presented also. © 2006 Elsevier B.V. All rights reserved.
منابع مشابه
2 7 Se p 20 06 A Note on ( 3 , 1 ) ∗ - Choosable Toroidal Graphs †
An (L, d)-coloring is a mapping φ that assigns a color φ(v) ∈ L(v) to each vertex v ∈ V (G) such that at most d neighbors of v receive colore φ(v). A graph is called (m, d)-choosable, if G admits an (L, d)-coloring for every list assignment L with |L(v)| ≥ m for all v ∈ V (G). In this note, it is proved that every toroidal graph, which contains no adjacent triangles and contains no 6-cycles and...
متن کاملA Note on (3, 1)∗-Choosable Toroidal Graphs
An (L, d)∗-coloring is a mapping φ that assigns a color φ(v) ∈ L(v) to each vertex v ∈ V (G) such that at most d neighbors of v receive colore φ(v). A graph is called (m, d)∗-choosable, if G admits an (L, d)∗-coloring for every list assignment L with |L(v)| ≥ m for all v ∈ V (G). In this note, it is proved that every toroidal graph, which contains no adjacent triangles and contains no 6-cycles ...
متن کاملEvery toroidal graph without triangles adjacent to $5$-cycles is DP-$4$-colorable
DP-coloring, also known as correspondence coloring, is introduced by Dvořák and Postle. It is a generalization of list coloring. In this paper, we show that every connected toroidal graph without triangles adjacent to 5-cycles has minimum degree at most three unless it is a 2-connected 4-regular graph with Euler characteristic (G) = 0. Consequently, every toroidal graph without triangles adjace...
متن کاملTotal coloring of 1-toroidal graphs with maximum degree at least 11 and no adjacent triangles
A total coloring of a graph G is an assignment of colors to the vertices and the edges of G such that every pair of adjacent/incident elements receive distinct colors. The total chromatic number of a graph G, denoted by χ′′(G), is the minimum number of colors needed in a total coloring of G. The most well-known Total Coloring Conjecture (TCC) says that every graph with maximum degree ∆ admits a...
متن کاملEdge choosability of planar graphs without small cycles
We investigate structural properties of planar graphs without triangles or without 4-cycles, and show that every triangle-free planar graph G is edge-( (G) + 1)-choosable and that every planar graph with (G) = 5 and without 4-cycles is also edge-( (G) + 1)-choosable. c © 2003 Elsevier B.V. All rights reserved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Applied Mathematics
دوره 155 شماره
صفحات -
تاریخ انتشار 2007