Contractible edges and removable edges in a graph with large minimum degree
نویسنده
چکیده
منابع مشابه
Removable Edges in Longest Cycles of 4-Connected Graphs
Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G e; second, for all vertices x of degree 3 in G e, delete x from G e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G e. If G e is 4-conn...
متن کاملSufficient conditions for maximally edge-connected and super-edge-connected
Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...
متن کاملMore on foxes
An edge in a k-connected graph G is called k-contractible if the graph G/e obtained from G by contracting e is k-connected. Generalizing earlier results on 3-contractible edges in spanning trees of 3-connected graphs, we prove that (except for the graphs Kk+1 if k ∈ {1, 2}) (a) every spanning tree of a k-connected triangle free graph has two k-contractible edges, (b) every spanning tree of a k-...
متن کاملOn removable cycles through every edge
Mader and Jackson independently proved that every 2-connected simple graph G with minimum degree at least four has a removable cycle, that is, a cycle C such that G\E(C) is 2-connected. This paper considers the problem of determining when every edge of a 2-connected graph G, simple or not, can be guaranteed to lie in some removable cycle. The main result establishes that if every deletion of tw...
متن کاملTotal domination in $K_r$-covered graphs
The inflation $G_{I}$ of a graph $G$ with $n(G)$ vertices and $m(G)$ edges is obtained from $G$ by replacing every vertex of degree $d$ of $G$ by a clique, which is isomorph to the complete graph $K_{d}$, and each edge $(x_{i},x_{j})$ of $G$ is replaced by an edge $(u,v)$ in such a way that $uin X_{i}$, $vin X_{j}$, and two different edges of $G$ are replaced by non-adjacent edges of $G_{I}$. T...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 35 شماره
صفحات -
تاریخ انتشار 2006