Nowhere-zero 5-flows

نویسندگان

  • Eckhard Steffen
  • Giuseppe Mazzuoccolo
چکیده

We prove that every cyclically 6-edge-connected cubic graph with oddness at most 4 has a nowhere-zero 5-flow. Therefore, a possible minimum counterexample to the 5-flow conjecture has oddness at least 6.

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

Cubic Graphs without a Petersen Minor Have Nowhere–zero 5–flows

We show that every bridgeless cubic graph without a Petersen minor has a nowhere-zero 5-flow. This approximates the known 4-flow conjecture of Tutte. A graph has a nowhere-zero k-flow if its edges can be oriented and assigned nonzero elements of the group Zk so that the sum of the incoming values equals the sum of the outcoming ones for every vertex of the graph. An equivalent definition we get...

متن کامل

Forbidden graphs and group connectivity

Many researchers have devoted themselves to the study of nowhere-zero flows and group connectivity. Recently, Thomassen confirmed the weak 3-flow conjecture, which was further improved by Lovász, Thomassen, Wu and Zhang who proved that every 6-edge-connected graph is Z3-connected. However, Conjectures 1 and 2 are still open. Conjecture 2 implies Conjecture 1 by a result of Kochol that reduces C...

متن کامل

Nowhere-Zero 5-Flows On Cubic Graphs with Oddness 4

Tutte’s 5-Flow Conjecture from 1954 states that every bridgeless graph has a nowhere-zero 5-flow. In 2004, Kochol proved that the conjecture is equivalent to its restriction on cyclically 6-edge connected cubic graphs. We prove that every cyclically 6-edge-connected cubic graph with oddness at most 4 has a nowhere-zero 5-flow.

متن کامل

Nowhere-zero flow polynomials

In this article we introduce the flow polynomial of a digraph and use it to study nowherezero flows from a commutative algebraic perspective. Using Hilbert’s Nullstellensatz, we establish a relation between nowhere-zero flows and dual flows. For planar graphs this gives a relation between nowhere-zero flows and flows of their planar duals. It also yields an appealing proof that every bridgeless...

متن کامل

Parity Subgraphs with Few Common Edges and Nowhere-Zero 5-Flow

A parity subgraph of a graph is a spanning subgraph such that the degrees of all vertices have the same parity in both the subgraph and the original graph. Let G be a cyclically 6-edge-connected cubic graph. Steffen (Intersecting 1-factors and nowhere-zero 5-flows 1306.5645, 2013) proved that G has a nowhere-zero 5-flow if G has two perfect matchings with at most two intersections. In this pape...

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