AbstractGiven four distinct vertices in a 4-connected planar graphG, we characterize when the graphGcontains aK4-subdivision with the given vertices as its degree three vertices. This result implies the following conjecture of Robertson and Thomas: a 5-connected planar graph has noK4-subdivision with specified degree three vertices, if and only if the four specified vertices are contained in a facial cycle in the unique plane embedding of the graph
A vertex v in a graph G = (V,E) is k-simplicial if the neighborhood N(v) of v can be vertex-covered ...
A simple quadrangulation of the sphere is a finite simple graph embedded on the sphere such that eve...
AbstractIn this note, we prove a structural theorem for planar graphs, namely that every planar grap...
Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-su...
A subdivision of a graph G, also known as a topological G and denoted by TG, is a graph obtained fro...
A fundamental theorem in graph theory states that any 3-connected graph contains a subdivision of K4...
We first prove that for every vertex x of a 4-connected graph G there exists a subgraph H in G isomo...
AbstractA well-known theorem of Kuratowski states that a graph is planar iff it contains no subdivis...
AbstractLet G be a 4-regular planar graph and suppose that G has a cycle decomposition S (i.e., each...
A graph G is almost 4-connected if it is simple, 3-connected, has at least five vertices, and V (G)...
Given a graph G=(V,E), four distinct vertices u_1, u_2, u_3, u_4 \in V and four natural numbers n_1,...
We show that every triconnected planar graph of maximum degree five is subhamiltonian planar. A grap...
AbstractA 3-valent graph G is cyclically n-connected provided one must cut at least n edges in order...
summary:In this paper it is proved that every $3$-connected planar graph contains a path on $3$ vert...
Lovász conjectured that every connected 4-regular planar graph G admits a realization as a system of...
A vertex v in a graph G = (V,E) is k-simplicial if the neighborhood N(v) of v can be vertex-covered ...
A simple quadrangulation of the sphere is a finite simple graph embedded on the sphere such that eve...
AbstractIn this note, we prove a structural theorem for planar graphs, namely that every planar grap...
Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-su...
A subdivision of a graph G, also known as a topological G and denoted by TG, is a graph obtained fro...
A fundamental theorem in graph theory states that any 3-connected graph contains a subdivision of K4...
We first prove that for every vertex x of a 4-connected graph G there exists a subgraph H in G isomo...
AbstractA well-known theorem of Kuratowski states that a graph is planar iff it contains no subdivis...
AbstractLet G be a 4-regular planar graph and suppose that G has a cycle decomposition S (i.e., each...
A graph G is almost 4-connected if it is simple, 3-connected, has at least five vertices, and V (G)...
Given a graph G=(V,E), four distinct vertices u_1, u_2, u_3, u_4 \in V and four natural numbers n_1,...
We show that every triconnected planar graph of maximum degree five is subhamiltonian planar. A grap...
AbstractA 3-valent graph G is cyclically n-connected provided one must cut at least n edges in order...
summary:In this paper it is proved that every $3$-connected planar graph contains a path on $3$ vert...
Lovász conjectured that every connected 4-regular planar graph G admits a realization as a system of...
A vertex v in a graph G = (V,E) is k-simplicial if the neighborhood N(v) of v can be vertex-covered ...
A simple quadrangulation of the sphere is a finite simple graph embedded on the sphere such that eve...
AbstractIn this note, we prove a structural theorem for planar graphs, namely that every planar grap...
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