Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: weight of an edge

Sortuj według:

Ogranicz wyniki do:

On Maximum Weight of a Bipartite Graph of Given Order and Size

100%

Horňák M., Jendrol’ S., Schiermeyer I.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 1

147-165

The weight of an edge xy of a graph is defined to be the sum of degrees of the vertices x and y. The weight of a graph G is the minimum of weights of edges of G. More than twenty years ago Erd˝os was interested in finding the maximum weight of a graph with n vertices and m edges. This paper presents a complete solution of a modification of the above problem in which a graph is required to be bipartite. It is shown that there is a function w*(n,m) such that the optimum weight is either w*(n,m) or w*(n,m) + 1.

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Paths of low weight in planar graphs

88%

Fabrici I., Harant J., Jendrol' S.

Discussiones Mathematicae Graph Theory

2008

tom 28

nr 1

121-135

The existence of paths of low degree sum of their vertices in planar graphs is investigated. The main results of the paper are: 1. Every 3-connected simple planar graph G that contains a k-path, a path on k vertices, also contains a k-path P such that for its weight (the sum of degrees of its vertices) in G it holds $w_G(P): = ∑_{u∈ V(P)} deg_G(u) ≤ (3/2)k² + 𝓞(k)$ 2. Every plane triangulation T that contains a k-path also contains a k-path P such that for its weight in T it holds $w_T(P): = ∑_{u∈ V(P)} deg_T(u) ≤ k² +13 k$ 3. Let G be a 3-connected simple planar graph of circumference c(G). If c(G) ≥ σ| V(G)| for some constant σ > 0 then for any k, 1 ≤ k ≤ c(G), G contains a k-path P such that $w_G(P) = ∑_{u∈ V(P)} deg_G(u) ≤ (3/σ + 3)k$.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Fabrici I.

1 Harant J.

1 Horňák M.

1 Jendrol' S.

1 Jendrol’ S.

1 Schiermeyer I.

1 2013

1 2008

Wyniki wyszukiwania

On Maximum Weight of a Bipartite Graph of Given Order and Size

Paths of low weight in planar graphs