Add to ORKGAbstract. Let a, b, c, d be four vertices in a graph G. A K4-minor rooted at a, b, c, d consists of four pairwise-disjoint pairwise-adjacent connected subgraphs of G, respectively containing a, b, c, d. We characterise precisely when G contains a K4-minor rooted at a, b, c, d by describing six classes of obstructions, which are the edge-maximal graphs containing noK4-minor rooted at a, b, c, d. The following two special cases illustrate the full characterisation: (1) A 4-connected non-planar graph contains a K4-minor rooted at a, b, c, d for every choice of a, b, c, d. (2) A 3-connected planar graph contains a K4-minor rooted at a, b, c, d if and only if a, b, c, d are not on a single face. 1
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
Archdeacon proved that projective-planar graphs are characterized by 35 excluded minors. Using this ...
Abstract. Let a, b, c, d be four vertices in a graph G. A K4-minor rooted at a, b, c, d consists of ...
AbstractA minimal point disconnecting set S of a graph G is a nontrivial m-separator, where m=|S|, i...
AbstractA graph is a minor of another if the first can be obtained from a subgraph of the second by ...
We provide a complete structural characterization of K2,4-minor-free graphs. The 3-connected K2,4-mi...
In this paper, we present three results: (1) Let G be a (k + 2)-connected non-(k - 3)-apex graph whe...
In this paper, we present three results: (1) Let G be a (k + 2)-connected non-(k - 3)-apex graph whe...
We first prove that for every vertex x of a 4-connected graph G there exists a subgraph H in G isomo...
AbstractA k-tree is formed from a k-complete graph by recursively adding a vertex adjacent to all ve...
AbstractThe purpose of this note is to give a connectivity condition for a graph to have a rooted co...
Let G be a 3-connected planar graph and let U ` V (G). It is shown that G contains a K 2;t minor suc...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
Archdeacon proved that projective-planar graphs are characterized by 35 excluded minors. Using this ...
Abstract. Let a, b, c, d be four vertices in a graph G. A K4-minor rooted at a, b, c, d consists of ...
AbstractA minimal point disconnecting set S of a graph G is a nontrivial m-separator, where m=|S|, i...
AbstractA graph is a minor of another if the first can be obtained from a subgraph of the second by ...
We provide a complete structural characterization of K2,4-minor-free graphs. The 3-connected K2,4-mi...
In this paper, we present three results: (1) Let G be a (k + 2)-connected non-(k - 3)-apex graph whe...
In this paper, we present three results: (1) Let G be a (k + 2)-connected non-(k - 3)-apex graph whe...
We first prove that for every vertex x of a 4-connected graph G there exists a subgraph H in G isomo...
AbstractA k-tree is formed from a k-complete graph by recursively adding a vertex adjacent to all ve...
AbstractThe purpose of this note is to give a connectivity condition for a graph to have a rooted co...
Let G be a 3-connected planar graph and let U ` V (G). It is shown that G contains a K 2;t minor suc...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
We show that for every n ≥ 3 there is some number m such that every 4-connected binary matroid with ...
Archdeacon proved that projective-planar graphs are characterized by 35 excluded minors. Using this ...