Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 5

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych:  1-planar graph
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

On properties of maximal 1-planar graphs

100%
Hudák D., Madaras T., Suzuki Y.
Discussiones Mathematicae Graph Theory
|
2012
|
tom 32
|
nr 4
737-747
EN
A graph is called 1-planar if there exists a drawing in the plane so that each edge contains at most one crossing. We study maximal 1-planar graphs from the point of view of properties of their diagrams, local structure and hamiltonicity.
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Light edges in 1-planar graphs with prescribed minimum degree

100%
Hudák D., Šugerek P.
Discussiones Mathematicae Graph Theory
|
2012
|
tom 32
|
nr 3
545-556
EN
A graph is called 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree δ ≥ 4 contains an edge with degrees of its endvertices of type (4, ≤ 13) or (5, ≤ 9) or (6, ≤ 8) or (7,7). We also show that for δ ≥ 5 these bounds are best possible and that the list of edges is minimal (in the sense that, for each of the considered edge types there are 1-planar graphs whose set of types of edges contains just the selected edge type).
3
Content available remote

On An Extremal Problem In The Class Of Bipartite 1-Planar Graphs

80%
Czap J., Przybyło J., Škrabuľáková E.
Discussiones Mathematicae Graph Theory
|
2016
|
tom 36
|
nr 1
141-151
EN
A graph G = (V, E) is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite 1-planar graphs with prescribed numbers of vertices in partite sets. Bipartite 1-planar graphs are known to have at most 3n − 8 edges, where n denotes the order of a graph. We show that maximal-size bipartite 1-planar graphs which are almost balanced have not significantly fewer edges than indicated by this upper bound, while the same is not true for unbalanced ones. We prove that the maximal possible size of bipartite 1-planar graphs whose one partite set is much smaller than the other one tends towards 2n rather than 3n. In particular, we prove that if the size of the smaller partite set is sublinear in n, then |E| = (2 + o(1))n, while the same is not true otherwise.
4
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

On local structure of 1-planar graphs of minimum degree 5 and girth 4

80%
Hudák D., Madaras T.
Discussiones Mathematicae Graph Theory
|
2009
|
tom 29
|
nr 2
385-400
EN
A graph is 1-planar if it can be embedded in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree 5 and girth 4 contains (1) a 5-vertex adjacent to an ≤ 6-vertex, (2) a 4-cycle whose every vertex has degree at most 9, (3) a $K_{1,4}$ with all vertices having degree at most 11.
5
Content available remote

On (p, 1)-total labelling of 1-planar graphs

70%
Zhang X., Yu Y., Liu G.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1424-1434
EN
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.