Group edge choosability of planar graphs without adjacent short cycles
نویسندگان
چکیده
In this paper, we aim to introduce the group version of edge coloring and list edge coloring, and prove that all 2-degenerate graphs along with some planar graphs without adjacent short cycles is group (∆(G) + 1)-edgechoosable while some planar graphs with large girth and maximum degree is group ∆(G)-edge-choosable.
منابع مشابه
Choosability and edge choosability of planar graphs without five cycles
It is proved that a planar graph G without five cycles is three degenerate, hence, four choosable, and it is also edge-(A( G) + l)h c oosable. @ 2002 Elsevier Science Ltd. All rights reserved. Keywords-Choosability, Edge choosability, Degeneracy, Planar graph.
متن کاملEdge-choosability and total-choosability of planar graphs with no adjacent 3-cycles
Let G be a planar graph with no two 3-cycles sharing an edge. We show that if ∆(G) ≥ 9, then χ′l(G) = ∆(G) and χ ′′ l (G) = ∆(G) + 1. We also show that if ∆(G) ≥ 6, then χ ′ l(G) ≤ ∆(G) + 1 and if ∆(G) ≥ 7, then χ′′ l (G) ≤ ∆(G) + 2. All of these results extend to graphs in the projective plane and when ∆(G) ≥ 7 the results also extend to graphs in the torus and Klein bottle. This second edge-c...
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 کاملOn Choosability with Separation of Planar Graphs with Forbidden Cycles
We study choosability with separation which is a constrained version of list coloring of graphs. A (k, d)-list assignment L of a graph G is a function that assigns to each vertex v a list L(v) of at least k colors and for any adjacent pair xy, the lists L(x) and L(y) share at most d colors. A graph G is (k, d)-choosable if there exists an L-coloring of G for every (k, d)-list assignment L. This...
متن کاملA Generalization of Kotzig's Theorem and Its Application
An edge of a graph is light when the sum of the degrees of its endvertices is at most 13. The well-known Kotzig Theorem states that every 3-connected planar graph contains a light edge. Later, Borodin [1] extended this result to the class of planar graphs of minimum degree at least 3. We deal with generalizations of these results for planar graphs of minimum degree 2. Borodin, Kostochka and Woo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1102.4980 شماره
صفحات -
تاریخ انتشار 2011