Random 4-regular graphs have claw-decompositions asymptotically almost surely

نویسندگان

  • Michelle Delcourt
  • Luke Postle
چکیده

In 2006, Barát and Thomassen conjectured that the edges of every planar 4-regular 4-edgeconnected graph can be decomposed into claws. Shortly afterward, Lai constructed a counterexample to this conjecture. Using the small subgraph conditioning method of Robinson and Wormald, we find that a random 4-regular graph has a claw-decomposition asymptotically almost surely, provided that the number of vertices is divisible by 3.

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 the girth of random Cayley graphs

We prove that random d-regular Cayley graphs of the symmetric group asymptotically almost surely have girth at least (logd−1 |G|) /2 and that random d-regular Cayley graphs of simple algebraic groups over Fq asymptotically almost surely have girth at least logd−1 |G|/ dim(G). For the symmetric p-groups the girth is between log log |G| and (log |G|) with α < 1. Several conjectures and open quest...

متن کامل

Colouring Random Regular Graphs

In a previous paper we showed that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6-regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random d-regular graph for other d between 5 and 10 inclusive is a.a.s. restricted to a range of two integer values...

متن کامل

Random Regular Graphs are not Asymptotically Gromov Hyperbolic

In this paper we prove that random d–regular graphs with d ≥ 3 have traffic congestion of the order O(n log3d−1(n)) where n is the number of nodes and geodesic routing is used. We also show that these graphs are not asymptotically δ–hyperbolic for any non–negative δ almost surely as n→∞.

متن کامل

Connectivity of random regular graphs generated by the pegging algorithm

We study the connectivity of random d-regular graphs which are recursively generated by an algorithm motivated by a peer to peer network. We show that these graphs are asymptotically almost surely d-connected for any even constant d ≥ 4.

متن کامل

Colouring Random 4-Regular Graphs

We show that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. The proof uses an efficient algorithm which a.a.s. 3colours a random 4-regular graph. The analysis includes use of the differential equation method, and exponential bounds on the tail of random variables associated with branching processes. A substantial part of the analysis applies to random d-r...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016