The fractional chromatic number of triangle-free subcubic graphs

نویسندگان

  • David G. Ferguson
  • Tomás Kaiser
  • Daniel Král
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Subcubic triangle-free graphs have fractional chromatic number at most 14/5

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].

متن کامل

The fractional chromatic number of Zykov products of graphs

Zykov designed one of the oldest known family of triangle-free graphs with arbitrarily high chromatic number. We determine the fractional chromatic number of the Zykov product of a family of graphs. As a corollary, we deduce that the fractional chromatic numbers of the Zykov graphs satisfy the same recurrence relation as those of the Mycielski graphs, that is an+1 = an + 1 an . This solves a co...

متن کامل

A χ-binding function for the class of {3K1, K1 ∪K4}-free graphs

We prove that the chromatic number of any {3K1,K1∪K4}-free graph is at most a factor 28/15 times its clique number. In order to prove this result we prove that any connected subcubic triangle-free graph G on n vertices has a matching of size at least (n− 1)/3, and we characterise the extremal graphs.

متن کامل

The fractional chromatic number of mycielski's graphs

The most familiar construction of graphs whose clique number is much smaller than their chromatic number is due to Mycielski, who constructed a sequence G n of triangle-free graphs with (G n ) = n. In this note, we calculate the fractional chromatic number of G n and show that this sequence of numbers satis es the unexpected recurrence a n+1 = a n + 1 a n .

متن کامل

Fractional Coloring of Triangle-Free Planar Graphs

We prove that every planar triangle-free graph on n vertices has fractional chromatic number at most 3− 1 n+1/3 .

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Eur. J. Comb.

دوره 35  شماره 

صفحات  -

تاریخ انتشار 2014