Graphs with no P̄7-minor
نویسندگان
چکیده
Let P̄7 denote the complement of a path on seven vertices. We determine all 4-connected graphs that do not contain P̄7 as a minor.
منابع مشابه
-λ coloring of graphs and Conjecture Δ ^ 2
For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V(G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G= H2. A function f:V(G) {0,1,2…, k} is called a coloring of G if for every pair of vertices x,yV(G) with d(x,y)=1 we have |f(x)-f(y)|2 an...
متن کاملRecent Excluded Minor Theorems for Graphs
A graph is a minor of another if the first can be obtained from a subgraph of the second by contracting edges. An excluded minor theorem describes the structure of graphs with no minor isomorphic to a prescribed set of graphs. Splitter theorems are tools for proving excluded minor theorems. We discuss splitter theorems for internally 4-connected graphs and for cyclically 5-connected cubic graph...
متن کاملK6-Minors in Triangulations on the Nonorientable Surface of Genus 3
It is easy to characterize graphs with no Kk-minors for any integer k ≤ 4, as follows. For k = 1, 2, the problem must be trivial, and for k = 3, 4, those graphs are forests and series-parallel graphs (i.e., graphs obtained from K3 by a sequence of replacing a vertex of degree 2 with a pair of parallel edges, or its inverse operation.) Moreover, Wagner formulated a fundamental characterization o...
متن کاملA Characterization of K2, 4-Minor-Free Graphs
We provide a complete structural characterization of K2,4-minor-free graphs. The 3-connected K2,4minor-free graphs consist of nine small graphs on at most eight vertices, together with a family of planar graphs that contains K4 and, for each n ≥ 5, 2n − 8 nonisomorphic graphs of order n. To describe the 2-connected K2,4-minor-free graphs we use xy-outerplanar graphs, graphs embeddable in the pl...
متن کامل1 Every longest circuit of a 3-connected, K3,3-minor free graph has a chord
Carsten Thomassen conjectured that every longest circuit in a 3-connected graph has a chord. We prove the conjecture for graphs having no K3,3 minor, and consequently for planar graphs. Carsten Thomassen made the following conjecture [1, 7], where a circuit denotes a connected 2-regular graph: Conjecture 1 (Thomassen) Every longest circuit of a 3-connected graph has a chord. That conjecture has...
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:
دوره شماره
صفحات -
تاریخ انتشار 2016