AbstractWe prove that each polyhedral triangular face free map G on a compact 2-dimensional manifold M with Euler characteristic χ(M) contains a k-path, i.e., a path on k vertices, such that each vertex of this path has, in G, degree at most (5/2)k if M is a sphere S0 and at most (k/2)⌊(5+49−24χ(M))/2⌋ if M≠S0 or does not contain any k-path. We show that for even k this bound is best possible. Moreover, we show that for any graph other than a path no similar estimation exists
AbstractA graph H has the property MT, if for all graphs G, G is H-free if and only if every minimal...
Continuing the author's earlier investigation, this paper studies the behavior of paths on (con...
Gallai conjectured that every connected graph on n vertices admits a path decomposition, i.e., a dec...
. We prove that each polyhedral triangular face free map G on a compact 2dimensional manifold M with...
AbstractWe prove that each polyhedral triangular face free map G on a compact 2-dimensional manifold...
AbstractWe have proved that each 3-connected multigraph G without loops and trivial 2-cycles embedde...
AbstractLet G(M) be the family of all 3-connected graphs which can be embedded in a compact 2-manifo...
summary:Let $P_k$ be a path on $k$ vertices. In an earlier paper we have proved that each polyhedral...
AbstractLet k≥ 2, be an integer and M be a closed two-manifold with Euler characteristic χ(M) ≤ 0. W...
summary:In this paper it is proved that every $3$-connected planar graph contains a path on $3$ vert...
AbstractIt is well known that every polyhedral map with large enough number of vertices contains a v...
AbstractIt is proved that every 3-connected planar graph G with δ(G)⩾4 either does not contain any p...
AbstractWe investigate the existence of subgraphs H of low degree sum wG(H) of their vertices in gra...
AbstractGiven a graphG, let ak-trestle ofGbe a 2-connected spanning subgraph ofGof maximum degree at...
A graph H has the property MT, if for all graphs G, G is H-free if and only if every minimal (chorda...
AbstractA graph H has the property MT, if for all graphs G, G is H-free if and only if every minimal...
Continuing the author's earlier investigation, this paper studies the behavior of paths on (con...
Gallai conjectured that every connected graph on n vertices admits a path decomposition, i.e., a dec...
. We prove that each polyhedral triangular face free map G on a compact 2dimensional manifold M with...
AbstractWe prove that each polyhedral triangular face free map G on a compact 2-dimensional manifold...
AbstractWe have proved that each 3-connected multigraph G without loops and trivial 2-cycles embedde...
AbstractLet G(M) be the family of all 3-connected graphs which can be embedded in a compact 2-manifo...
summary:Let $P_k$ be a path on $k$ vertices. In an earlier paper we have proved that each polyhedral...
AbstractLet k≥ 2, be an integer and M be a closed two-manifold with Euler characteristic χ(M) ≤ 0. W...
summary:In this paper it is proved that every $3$-connected planar graph contains a path on $3$ vert...
AbstractIt is well known that every polyhedral map with large enough number of vertices contains a v...
AbstractIt is proved that every 3-connected planar graph G with δ(G)⩾4 either does not contain any p...
AbstractWe investigate the existence of subgraphs H of low degree sum wG(H) of their vertices in gra...
AbstractGiven a graphG, let ak-trestle ofGbe a 2-connected spanning subgraph ofGof maximum degree at...
A graph H has the property MT, if for all graphs G, G is H-free if and only if every minimal (chorda...
AbstractA graph H has the property MT, if for all graphs G, G is H-free if and only if every minimal...
Continuing the author's earlier investigation, this paper studies the behavior of paths on (con...
Gallai conjectured that every connected graph on n vertices admits a path decomposition, i.e., a dec...