On graphs without P5 and P5_

نویسندگان

  • Jean-Luc Fouquet
  • Vassilis Giakoumakis
  • Frédéric Maire
  • Henri Thuillier
چکیده

We extend results due to Z.Bll azsik et al. on graphs with no induced C 4 and 2K 2 to the self-complementary class of (P 5 ; P 5)-free graphs. Moreover, we obtain an O(! 2)-binding function for this last class of graphs, answering thus partially a question of A. Gyy arff as.

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

On mirror nodes in graphs without long induced paths

The notion of mirror nodes, first introduced by Fomin, Grandoni and Kratsch in 2006, turned out to be a useful item for their design of an algorithm for the maximum independent set problem (MIS). Given two nodes u, v of a graph G = (V, E) with distG(u, v) = 2, u is called a mirror of v if N(v) \N(u) induces a (possibly empty) clique. In order to have a well defined term, we add that every compl...

متن کامل

Graphs Without Induced

Zverovich [Discuss. Math. Graph Theory 23 (2003), 159–162.] has proved that the domination number and connected domination number are equal on all connected graphs without induced P5 and C5. Here we show (with an independent proof) that the following stronger result is also valid: Every P5-free and C5-free connected graph contains a minimum-size dominating set that induces a complete subgraph.

متن کامل

On (P5, diamond)-free graphs

We study the stability number, chromatic number and clique cover of graphs with no induced P5 and diamonds. In particular, we provide a way to obtain all imperfect (P5, diamond)-free graphs by iterated point multiplication or substitution from a /nite collection of small basic graphs. Corollaries of this and other structural properties, among which a result of Bacs1 o and Tuza, are (i) combinat...

متن کامل

On variations of P4-sparse graphs

Hoàng defined the P4-sparse graphs as the graphs where every set of five vertices induces at most one P4. These graphs attracted considerable attention in connection with the P4-structure of graphs and the fact that P4-sparse graphs have bounded clique-width. Fouquet and Giakoumakis generalized this class to the nicely structured semi-P4-sparse graphs being the (P5, co-P5, co-chair)-free graphs...

متن کامل

Polynomial Cases for the Vertex Coloring Problem

The computational complexity of the Vertex Coloring problem is known for all hereditary classes of graphs defined by forbidding two connected five-vertex induced subgraphs, except for seven cases. We prove the polynomial-time solvability of four of these problems: for (P5, dart)-free graphs, (P5, banner)-free graphs, (P5, bull)-free graphs, and (fork, bull)-free graphs.

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:
  • Discrete Mathematics

دوره 146  شماره 

صفحات  -

تاریخ انتشار 1995