A list version of Dirac's theorem on the number of edges in colour-critical graphs

نویسندگان

  • Alexandr V. Kostochka
  • Michael Stiebitz
چکیده

One of the basic results in graph colouring is Brooks' theorem [R.

برای دانلود رایگان 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

A short proof of Dirac's theorem on the number of edges in chromatically critical graphs

A short proof is presented for a theorem of G. A. Dirac (1974) giving a lower bound for the number of edges of a k-critical graph on a given number of vertices and describing all non-complete k-critical graphs with minimum edge excess.

متن کامل

On the saturation number of graphs

Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. In this paper we study the saturation numbe...

متن کامل

On the variable sum exdeg index and cut edges of graphs

The variable sum exdeg index of a graph G is defined as $SEI_a(G)=sum_{uin V(G)}d_G(u)a^{d_G(u)}$, where $aneq 1$ is a positive real number,  du(u) is the degree of a vertex u ∈ V (G). In this paper, we characterize the graphs with the extremum variable sum exdeg index among all the graphs having a fixed number of vertices and cut edges, for every a>1.

متن کامل

Gallai's problem on Dirac's construction

Youngs, D.A., Gallai’s problem on Dirac’s construction, Discrete Mathematics 101 (1992) 343-350. It is thought that T. Gallai posed the following problem concerning a construction due to G.A. Dirac: suppose that a graph K consists of disjoint subgraphs G and Hand a set of edges joining them. If each of G, H, and K are colour critical graphs, under what circumstances is it then true that the joi...

متن کامل

Improved lower bounds on the number of edges in list critical and online list critical graphs

We prove that every k-list-critical graph (k ≥ 7) on n ≥ k + 2 vertices has at least 1 2 ( k − 1 + k−3 (k−c)(k−1)+k−3 ) n edges where c = (k − 3) ( 1 2 − 1 (k−1)(k−2) ) . This improves the bound established by Kostochka and Stiebitz [13]. The same bound holds for online k-list-critical graphs, improving the bound established by Riasat and Schauz [16]. Both bounds follow from a more general resu...

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

عنوان ژورنال:
  • Journal of Graph Theory

دوره 39  شماره 

صفحات  -

تاریخ انتشار 2002