Decomposing series-parallel graphs into paths of length 3 and triangles

نویسنده

  • Martin Merker
چکیده

An old conjecture by Jünger, Reinelt and Pulleyblank states that every 2-edgeconnected planar graph can be decomposed into paths of length 3 and triangles, provided its size is divisible by 3. We prove the conjecture for a class of planar graphs including all 2-edge-connected series-parallel graphs. We also present a 2edge-connected non-planar graph that can be embedded on the torus and admits no decomposition into paths of length 3 and triangles.

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

Decomposing Highly Connected Graphs into Paths of Length Five

Barát and Thomassen (2006) posed the following decomposition conjecture: for each tree T , there exists a natural number kT such that, if G is a kT -edge-connected graph and |E(G)| is divisible by |E(T )|, then G admits a decomposition into copies of T . In a series of papers, Thomassen verified this conjecture for stars, some bistars, paths of length 3, and paths whose length is a power of 2. ...

متن کامل

Decomposing Graphs into Long Paths

It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C3, C4, C5, and K4 − e have no such decompositions. We construct an infinite sequence {Fi}∞i=0 of nondecomposable graphs. On the other hand, we prove that every...

متن کامل

Decomposing block-intersection graphs of Steiner triple systems into triangles

The problem of decomposing the block intersection graph of a Steiner triple system into triangles is considered. In the case when the block intersection graph has even degree, this is completely solved, while when the block intersection graph has odd degree, removal of some spanning subgraph of odd degree is necessary before the rest can be decomposed into triangles. In this case, some decompos...

متن کامل

Gaussian Z Channel with Intersymbol Interference

In this paper, we derive a capacity inner bound for a synchronous Gaussian Z channel with intersymbol interference (ISI) under input power constraints. This is done by converting the original channel model into an n-block memoryless circular Gaussian Z channel (n-CGZC) and successively decomposing the n-block memoryless channel into a series of independent parallel channels in the frequency dom...

متن کامل

Minimum convex piecewise linear cost tension problem on quasi-k series-parallel graphs

This article proposes an extension, combined with the out-of-kilter technique, of the aggregation method (that solves the minimum convex piecewise linear cost tension problem, or CPLCT, on series-parallel graphs) to solve CPLCT on quasi series-parallel graphs. To make this algorithm efficient, the key point is to find a "good" way of decomposing the graph into series-parallel subgraphs. Decompo...

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:
  • Electronic Notes in Discrete Mathematics

دوره 49  شماره 

صفحات  -

تاریخ انتشار 2015