Temat: bipartite digraph - Prolib Integro

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Tytuł:: On the Optimality of 3-Restricted Arc Connectivity for Digraphs and Bipartite Digraphs
Autorzy:: Zhang, Yaoyao
Meng, Jixiang
Tematy:: restricted arc-connectivity
bipartite digraph
optimality
digraph
network; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32361733.pdf Link otwiera się w nowym oknie
Opis:: Let D be a strong digraph. An arc subset S is a k-restricted arc cut of D if D − S has a strong component D′ with order at least k such that D\V (D′) contains a connected subdigraph with order at least k. If such a k-restricted arc cut exists in D, then D is called λ^k-connected. For a λ^k-connected digraph D, the k-restricted arc connectivity, denoted by λ^k(D), is the minimum cardinality over all k-restricted arc cuts of D. It is known that for many digraphs λ^k(D) ≤ ξ^k(D), where ξ^k(D) denotes the minimum k-degree of D. D is called λ^k-optimal if λ^k(D) = ξ^k(D). In this paper, we will give some sufficient conditions for digraphs and bipartite digraphs to be λ³-optimal.
Dostawca treści:: Biblioteka Nauki

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Tytuł:: Cycles of many lengths in balanced bipartite digraphs on dominating and dominated degree conditions
Autorzy:: Wang, Ruixia
Wu, Linxin
Tematy:: bipartite digraph
degree sum
bipancyclicity
hamiltonian cycle; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/59882203.pdf Link otwiera się w nowym oknie
Opis:: In 2017, Adamus proved that a strong balanced bipartite digraph of order $2a$ with $a\geq 3$ is hamiltonian, if $d(u)+d(v)\geq 3a$ for every pair of dominating or dominated vertices $\{u,v\}$. In this paper, we characterize all non-hamiltonian bipartite digraphs when $d(u)+d(v)\geq 3a-1$ for every pair of dominating or dominated vertices $\{u,v\}$, consisting of one infinite family and four exceptional bipartite digraphs of order six. Using this result, we also prove that a strong balanced bipartite digraph of order $2a$ with $a\geq 4$ contains all cycles of lengths $2, 4, \ldots, 2a-2$ except for a single bipartite digraph, and also contains a hamiltonian path, if $d(u)+d(v)\geq 3a-1$ for every pair of dominating or dominated vertices $\{u, v\}$. The bounds for $3a-1$ in two results are sharp. This partly settles the following problem when $l=a-1$ proposed by Adamus [A Meyniel-type condition for bipancyclicity in balanced bipartitie digraphs, Graphs Combin. 34 (2018) 703–709]. Whether for every $1\le l< a$ there is a $k(l)$, $k(l)\ge 1$, such that every strong balanced bipartite digraph of order $2a$ contains cycles of lengths $2, 4, \ldots, 2l$, whenever $d(u)+d(v)\ge 3a-k(l)$ for every pair of dominating or dominated vertices $\{u, v\}$.
Dostawca treści:: Biblioteka Nauki

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