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On the Non-(p−1)-Partite Kp-Free Graphs

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Amin K., Faudree J., Gould R. J., Sidorowicz E.

Discussiones Mathematicae Graph Theory

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2013

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tom 33

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nr 1

9-23

EN

We say that a graph G is maximal Kp-free if G does not contain Kp but if we add any new edge e ∈ E(G) to G, then the graph G + e contains Kp. We study the minimum and maximum size of non-(p − 1)-partite maximal Kp-free graphs with n vertices. We also answer the interpolation question: for which values of n and m are there any n-vertex maximal Kp-free graphs of size m?

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Weakly P-saturated graphs

100%

Borowiecki M., Sidorowicz E.

Discussiones Mathematicae Graph Theory

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2002

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tom 22

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nr 1

17-29

EN

For a hereditary property 𝓟 let $k_{𝓟}(G)$ denote the number of forbidden subgraphs contained in G. A graph G is said to be weakly 𝓟-saturated, if G has the property 𝓟 and there is a sequence of edges of G̅, say $e₁,e₂,...,e_l$, such that the chain of graphs $G = G₀ ⊂ G_0 + e₁ ⊂ G₁ + e₂ ⊂ ... ⊂ G_{l-1} + e_l = G_l = K_n(G_{i+1} = G_i + e_{i+1})$ has the following property: $k_{𝓟}(G_{i+1}) > k_{𝓟}(G_i)$, 0 ≤ i ≤ l-1. In this paper we shall investigate some properties of weakly saturated graphs. We will find upper bound for the minimum number of edges of weakly 𝓓ₖ-saturated graphs of order n. We shall determine the number wsat(n,𝓟) for some hereditary properties.

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An advance in infinite graph models for the analysis of transportation networks

88%

Cera M., Fedriani E.

International Journal of Applied Mathematics and Computer Science

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2016

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tom 26

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nr 4

855-870

EN

This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph. It also relates the new results with the corresponding situations for the finite case. In particular, concepts from ‘finite' graph theory, like the average degree and the extremal number, are generalized and computed for some specific cases. Finally, some applications of infinite graphs to the transportation of dangerous goods are presented; they involve the analysis of networks and percolation thresholds.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 International Journal of Applied Mathematics and Computer Science

2 Sidorowicz E.

1 Amin K.

1 Borowiecki M.

1 Cera M.

1 Faudree J.

1 Fedriani E.

1 Gould R. J.

1 2016

1 2013

1 2002

On the Non-(p−1)-Partite Kp-Free Graphs

Weakly P-saturated graphs

An advance in infinite graph models for the analysis of transportation networks