AbstractIn this note, we prove a structural theorem for planar graphs, namely that every planar graph has one of four possible configurations: (1) a vertex of degree 1, (2) intersecting triangles, (3) an edge xy with d(x)+d(y)≤9, (4) a 2-alternating cycle. Applying this theorem, new moderate results on edge choosability, total choosability, edge-partitions and linear arboricity of planar graphs are obtained
AbstractAnouterplanargraph is one that can be embedded in the plane so that all of the vertices lie ...
Maximal planar graph refers to the planar graph with the most edges, which means no more edges can b...
AbstractThe vertex-arboricity a(G) of a graph G is the minimum number of subsets into which the set ...
AbstractWe investigate structural properties of planar graphs without triangles or without 4-cycles,...
AbstractSome structural properties of planar graphs without 4-cycles are investigated. By the struct...
An edge of a graph is light when the sum of the degrees of its end-vertices is at most 13. The well-...
Collected in this volume are most of the important theorems and algorithms currently known for plana...
Let G be a planar graph with no two 3-cycles sharing an edge. We show that if ∆(G) ≥ 9, then χ′l(G)...
Abstract. A graph is called 1-planar if it can be drawn on the plane so that each edge is crossed by...
International audienceWe give a short proof of the following theorem due to Borodin (1990). Every pl...
AbstractThe vertex-arboricity a(G) of a graph G is the minimum number of subsets into which vertex s...
All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Det...
AbstractWe give a short proof of the following theorem due to Borodin (1990) [2]. Every planar graph...
Let G be a planar graph with no two 3-cycles sharing an edge. We show that if Δ(G) ≥ 9, then χ'ₗ(G) ...
AbstractIt is proved that a planar graph G without five cycles is three degenerate, hence, four choo...
AbstractAnouterplanargraph is one that can be embedded in the plane so that all of the vertices lie ...
Maximal planar graph refers to the planar graph with the most edges, which means no more edges can b...
AbstractThe vertex-arboricity a(G) of a graph G is the minimum number of subsets into which the set ...
AbstractWe investigate structural properties of planar graphs without triangles or without 4-cycles,...
AbstractSome structural properties of planar graphs without 4-cycles are investigated. By the struct...
An edge of a graph is light when the sum of the degrees of its end-vertices is at most 13. The well-...
Collected in this volume are most of the important theorems and algorithms currently known for plana...
Let G be a planar graph with no two 3-cycles sharing an edge. We show that if ∆(G) ≥ 9, then χ′l(G)...
Abstract. A graph is called 1-planar if it can be drawn on the plane so that each edge is crossed by...
International audienceWe give a short proof of the following theorem due to Borodin (1990). Every pl...
AbstractThe vertex-arboricity a(G) of a graph G is the minimum number of subsets into which vertex s...
All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Det...
AbstractWe give a short proof of the following theorem due to Borodin (1990) [2]. Every planar graph...
Let G be a planar graph with no two 3-cycles sharing an edge. We show that if Δ(G) ≥ 9, then χ'ₗ(G) ...
AbstractIt is proved that a planar graph G without five cycles is three degenerate, hence, four choo...
AbstractAnouterplanargraph is one that can be embedded in the plane so that all of the vertices lie ...
Maximal planar graph refers to the planar graph with the most edges, which means no more edges can b...
AbstractThe vertex-arboricity a(G) of a graph G is the minimum number of subsets into which the set ...
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