Temat: implicit degree - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Spanning trees with a bounded number of leaves
Autorzy:: Cai, J.
Flandrin, E.
Li, H.
Sun, Q.
Powiązania:: https://bibliotekanauki.pl/articles/255239.pdf
Data publikacji:: 2017
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: spanning tree
implicit degree
leaves
Opis:: n 1998, H. Broersma and H. Tuinstra proved that: Given a connected graph G with n ≥ 3 vertices, if d(u) + d(y) ≥n — k + 1 for all non-adjacent vertices u and v of G (k ≥ 1), then G has a spanning tree with at most k leaves. In this paper, we generalize this result by using implicit degree sum condition of t (2≤ t ≤k) independent vertices and we prove what follows: Let G be a connected graph on n ≥ 3 vertices and k ≥ 2 be an integer. If the implicit degree sum of any t independent vertices is at least [formula] for (k≥ t ≥ 2), then G has a spanning tree with at most k leaves.
Źródło:: Opuscula Mathematica; 2017, 37, 4; 501-508
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: An implicit weighted degree condition for heavy cycles
Autorzy:: Cai, Junqing
Li, Hao
Ning, Wantao
Powiązania:: https://bibliotekanauki.pl/articles/30148719.pdf
Data publikacji:: 2014-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: weighted graph
hamiltonian cycles
heavy cycles
implicit degree
implicit weighted degree
Opis:: For a vertex v in a weighted graph G, id^w(v) denotes the implicit weighted degree of v. In this paper, we obtain the following result: Let G be a 2-connected weighted graph which satisfies the following conditions: (a) The implicit weighted degree sum of any three independent vertices is at least t; (b) w(xz) = w(yz) for every vertex z ∈ N(x) ∩ N(y) with xy /∈ E(G); (c) In every triangle T of G, either all edges of T have different weights or all edges of T have the same weight. Then G contains either a hamiltonian cycle or a cycle of weight at least 2t/3. This generalizes the result of Zhang et al. [9].
Źródło:: Discussiones Mathematicae Graph Theory; 2014, 34, 4; 801-810
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: On Implicit Heavy Subgraphs and Hamiltonicity of 2-Connected Graphs
Autorzy:: Zheng, Wei
Wideł, Wojciech
Wang, Ligong
Powiązania:: https://bibliotekanauki.pl/articles/32083821.pdf
Data publikacji:: 2021-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: implicit degree
implicit o-heavy
implicit f-heavy
implicit c-heavy
Hamilton cycle
Opis:: A graph G of order n is implicit claw-heavy if in every induced copy of K1,3 in G there are two non-adjacent vertices with sum of their implicit degrees at least n. We study various implicit degree conditions (including, but not limiting to, Ore- and Fan-type conditions) imposing of which on specific induced subgraphs of a 2-connected implicit claw-heavy graph ensures its Hamiltonicity. In particular, we improve a recent result of [X. Huang, Implicit degree condition for Hamiltonicity of 2-heavy graphs, Discrete Appl. Math. 219 (2017) 126–131] and complete the characterizations of pairs of o-heavy and f-heavy subgraphs for Hamiltonicity of 2-connected graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2021, 41, 1; 167-181
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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