Results 41 to 50 of about 998 (73)

Cycles in Random Bipartite Graphs [PDF]

, 2013
In this paper we study cycles in random bipartite graph $G(n,n,p)$. We prove that if $p\gg n^{-2/3}$, then $G(n,n,p)$ a.a.s. satisfies the following. Every subgraph $G'\subset G(n,n,p)$ with more than $(1+o(1))n^2p/2$ edges contains a cycle of length $t$
Shang, Yilun
core  

A Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs

Discussiones Mathematicae Graph Theory, 2020
Let 𝒫 be a property of a graph. A graph G is said to be locally 𝒫, if the subgraph induced by the open neighbourhood of every vertex in G has property 𝒫. Ryjáček conjectures that every connected, locally connected graph is weakly pancyclic.
Tang Long, Vumar Elkin
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Dirac type condition and Hamiltonian graphs [PDF]

, 2011
2010 Mathematics Subject Classification: 05C38, 05C45.In 1952, Dirac introduced the degree type condition and proved that if G is a connected graph of order n і 3 such that its minimum degree satisfies d(G) і n/2, then G is Hamiltonian.
Zhao, Kewen
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Dense Arbitrarily Partitionable Graphs

Discussiones Mathematicae Graph Theory, 2016
A graph G of order n is called arbitrarily partitionable (AP for short) if, for every sequence (n1, . . . , nk) of positive integers with n1 + ⋯ + nk = n, there exists a partition (V1, . . .
Kalinowski Rafał, Pilśniak Monika, Schiermeyer Ingo, Woźniak Mariusz   +3 more
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2-Spanning Cyclability Problems of Some Generalized Petersen Graphs

Discussiones Mathematicae Graph Theory, 2020
A graph G is called r-spanning cyclable if for every r distinct vertices v1, v2, . . . , vr of G, there exists r cycles C1, C2, . . . , Cr in G such that vi is on Ci for every i, and every vertex of G is on exactly one cycle Ci.
Yang Meng-Chien, Hsu Lih-Hsing, Hung Chun-Nan, Cheng Eddie   +3 more
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Cubic graphs with large circumference deficit [PDF]

, 2013
The circumference $c(G)$ of a graph $G$ is the length of a longest cycle. By exploiting our recent results on resistance of snarks, we construct infinite classes of cyclically $4$-, $5$- and $6$-edge-connected cubic graphs with circumference ratio $c(G)/|
Mazák, Ján, Máčajová, Edita
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Distance-Local Rainbow Connection Number

Discussiones Mathematicae Graph Theory, 2022
Under an edge coloring (not necessarily proper), a rainbow path is a path whose edge colors are all distinct. The d-local rainbow connection number lrcd(G) (respectively, d-local strong rainbow connection number lsrcd(G)) is the smallest number of colors
Septyanto Fendy, Sugeng Kiki A.
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Cyclic Permutations in Determining Crossing Numbers

Discussiones Mathematicae Graph Theory, 2022
The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. Recently, the crossing numbers of join products of two graphs have been studied.
Klešč Marián, Staš Michal
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On the planarity of line Mycielskian graph of a graph

Ratio Mathematica, 2020
The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤  i ≤  q and e, then for 1 ≤  i ≤  q , joining ei' to the neighbours of ei  and  to e.
Keerthi G. Mirajkar, Anuradha V Deshpande   +1 more
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Enumeration of weighted paths on a digraph and block hook determinant

Special Matrices, 2021
In this article, we evaluate determinants of “block hook” matrices, which are block matrices consist of hook matrices. In particular, we deduce that the determinant of a block hook matrix factorizes nicely.
Bera Sudip
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