Cyclically 5-edge connected non-bicritical critical snarks
نویسندگان
چکیده
Snarks are bridgeless cubic graphs with chromatic index χ = 4. A snark G is called critical if χ(G − {v, w}) = 3, for any two adjacent vertices v and w. For any k ≥ 2 we construct cyclically 5-edge connected critical snarks G having an independent set I of at least k vertices such that χ(G − I) = 4. For k = 2 this solves a problem of Nedela and Škoviera [6].
منابع مشابه
Non-Bicritical Critical Snarks
Snarks are cubic graphs with chromatic index 0 = 4. A snark G is called critical if 0 (G?fv; wg) = 3 for any two adjacent vertices v and w, and it is called bicritical if 0 (G ? fv; wg) = 3 for any two vertices v and w. We construct innnite families of critical snarks which are not bicritical. This solves a problem stated by Nedela and Skoviera in 7].
متن کاملA note on Fouquet-Vanherpe’s question and Fulkerson conjecture
The excessive index of a bridgeless cubic graph $G$ is the least integer $k$, such that $G$ can be covered by $k$ perfect matchings. An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless cubic graph has excessive index at most five. Clearly, Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5, so Fouquet and Vanherpe as...
متن کاملOdd 2-factored snarks
A snark is a cubic cyclically 4–edge connected graph with edge chromatic number four and girth at least five. We say that a graph G is odd 2–factored if for each 2–factor F of G each cycle of F is odd. In this paper, we present a method for constructing odd 2–factored snarks. In particular, we construct two new odd 2–factored snarks that disprove a conjecture by some of the authors. Moreover, w...
متن کاملPermutation snarks
A permutation snark is a cubic graph with no 3-edge-colouring that contains a 2-factor consisting of two induced circuits. In the talk we analyse the basic properties of permutation snarks, focusing on the structure of edge-cuts of size 4 and 5. As an application of our knowledge we provide rich families of cyclically 4edge-connected and 5-edge-connected permutation snarks of order 8n+2 for eac...
متن کاملImproved bounds for the shortness coefficient of cyclically 4-edge connected cubic graphs and snarks
We present a construction which shows that there is an infinite set of cyclically 4-edge connected cubic graphs on n vertices with no cycle longer than c4n for c4 = 12 13 , and at the same time prove that a certain natural family of cubic graphs cannot be used to lower the shortness coefficient c4 to 0. The graphs we construct are snarks so we get the same upper bound for the shortness coeffici...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 19 شماره
صفحات -
تاریخ انتشار 1999