Subcubic triangle-free graphs have fractional chromatic number at most 14/5
نویسندگان
چکیده
We prove that every subcubic triangle-free graph has fractional chromatic number at most 14/5, thus confirming a conjecture of Heckman and Thomas [A new proof of the independence ratio of triangle-free cubic graphs. Discrete Math. 233 (2001), 233–237].
منابع مشابه
The fractional chromatic number of triangle-free subcubic graphs
Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14/5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free subcubic graph is at most 32/11 ≈ 2.909.
متن کاملN ov 2 01 0 The Fractional Chromatic Number of Triangle - free Graphs with ∆ ≤ 3
Let G be any triangle-free graph with maximum degree ∆ ≤ 3. Staton proved that the independence number of G is at least 5 14 n. Heckman and Thomas conjectured that Staton’s result can be strengthened into a bound on the fractional chromatic number of G, namely χf (G) ≤ 14 5 . Recently, Hatami and Zhu proved χf (G) ≤ 3− 3 64 . In this paper, we prove χf (G) ≤ 3− 3 43 .
متن کاملThe fractional chromatic number of triangle-free graphs with Δ<3
Let G be a triangle-free graph with maximum degree at most 3. Staton proved that the independence number of G is at least 5 14 |V (G)|. Heckman and Thomas conjectured that Staton’s result can be strengthened into a bound on the fractional chromatic number of G, namely χf (G) ≤ 14 5 . Recently, Hatami and Zhu proved that χf (G) ≤ 3 − 3 64 . In this paper, we prove χf (G) ≤ 3 − 3 43 . © 2012 Else...
متن کاملOn minimal triangle-free 6-chromatic graphs
A graph with chromatic number k is called k-chromatic. Using computational methods, we show that the smallest triangle-free 6-chromatic graphs have at least 32 and at most 40 vertices. We also determine the complete set of all triangle-free 5-chromatic graphs up to 23 vertices and all triangle-free 5-chromatic graphs on 24 vertices with maximum degree at most 7. This implies that Reed’s conject...
متن کاملBipartite subgraphs of triangle-free subcubic graphs
Suppose G is a graph with n vertices and m edges. Let n′ be the maximum number of vertices in an induced bipartite subgraph of G and let m′ be the maximum number of edges in a spanning bipartite subgraph of G. Then b(G) = m′/m is called the bipartite density of G, and b∗(G) = n′/n is called the bipartite ratio of G. This paper proves that every 2connected triangle-free subcubic graph, apart fro...
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:
- J. London Math. Society
دوره 89 شماره
صفحات -
تاریخ انتشار 2014