Colouring of ( P3 ∪ P2)-free graphs

نویسندگان

  • Arpitha P. Bharathi
  • Sheshayya A. Choudum
چکیده

The class of 2K2-free graphs and its various subclasses have been studied in a variety of contexts. In this paper, we are concerned with the colouring of (P3 ∪P2)-free graphs, a super class of 2K2-free graphs. We derive a O(ω3) upper bound for the chromatic number of (P3 ∪P2)-free graphs, and sharper bounds for (P3 ∪P2, diamond)-free graphs, where ω denotes the clique number. By applying similar proof techniques we obtain chromatic bounds for (2K2, diamond)-free graphs. The last two classes are perfect if ω ≥ 5 and ≥ 4 respectively.

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

Partitioning a graph into disjoint cliques and a triangle-free graph

A (P3-free, K3-free)-colouring of a graph G = (V, E) is a partition of V = A ∪ B such that G[A] is P3-free and G[B] is K3-free. This problem is known to be NP-complete even when restricted to planar graphs and perfect graphs. In this paper, we provide a finite list of 17 forbidden induced subgraphs for cographs with a (P3-free, K3-free)colouring. This yields a linear time recognition algorithm.

متن کامل

Hereditary Graph Classes: When the Complexities of Colouring and Clique Cover Coincide⋆

A graph is (H1,H2)-free for a pair of graphsH1, H2 if it contains no induced subgraph isomorphic toH1 orH2. In 2001, Král’, Kratochvíl, Tuza, and Woeginger initiated a study into the complexity of Colouring for (H1,H2)free graphs. Since then, others have tried to complete their study, but many cases remain open. We focus on those (H1,H2)-free graphs where H2 is H1, the complement of H1. As thes...

متن کامل

Colouring on Hereditary Graph Classes Closed under Complementation

A graph is (H1,H2)-free for a pair of graphsH1, H2 if it contains no induced subgraph isomorphic toH1 orH2. In 2001, Král’, Kratochvíl, Tuza, and Woeginger initiated a study into the complexity of Colouring for (H1,H2)free graphs. Since then, others have tried to complete their study, but many cases remain open. We focus on those (H1,H2)-free graphs where H2 is H1, the complement of H1. As thes...

متن کامل

Generalised game colouring of graphs

We consider the version of a colouring game introduced by Bodlaender [On the complexity of some colorings games, Internat. J. Found. Comput. Sci. 2 (1991) 133–147]. We combine the concepts: this game and the generalised colouring of graphs as follows. The two players are Alice and Bob and they play alternatively with Alice having the first move. Let be given a graph G and an ordered set of here...

متن کامل

On colouring (2P2, H)-free and (P5, H)-free graphs

The Colouring problem asks whether the vertices of a graph can be coloured with at most $k$ colours for a given integer $k$ in such a way that no two adjacent vertices receive the same colour. A graph is $(H_1,H_2)$-free if it has no induced subgraph isomorphic to $H_1$ or $H_2$. A connected graph $H_1$ is almost classified if Colouring on $(H_1,H_2)$-free graphs is known to be polynomial-time ...

متن کامل

ذخیره در منابع من

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


  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:
  • Graphs and Combinatorics

دوره 34  شماره 

صفحات  -

تاریخ انتشار 2018