scholarly journals Maximum and Minimum Degree Conditions for Embedding Trees

2020 ◽  
Vol 34 (4) ◽  
pp. 2108-2123
Author(s):  
Guido Besomi ◽  
Matías Pavez-Signé ◽  
Maya Stein
Keyword(s):  
Minimum Degree ◽  
Degree Conditions ◽  
Maximum And Minimum Degree

scholarly journals In-situ Desaturation Tests by Electrolysis for Liquefaction Mitigation

2021 ◽  
Author(s):  
Runze Chen ◽  
Yumin Chen ◽  
Hanlong Liu ◽  
Kunxian Zhang ◽  
Ying Zhou ◽  
...  
Keyword(s):  
Minimum Degree ◽  
Electricity Consumption ◽  
Potential Method ◽  
Economic Benefits ◽  
Degree Of Saturation ◽  
Test Results ◽  
Liquefaction Resistance ◽  
The Difference ◽  
Maximum And Minimum Degree

Electrolytic desaturation is a potential method for improving the liquefaction resistance of the liquefiable foundation by reducing the soil saturation. In this study, in-situ desaturation tests were performed to investigate the resistivity of soil at different depth and the water level of the foundation under different current. The test results show that at constant currents of 1 A (Ampere, unit of the direct current), 2 A and 3 A, the saturation of the treated foundation reached 87%, 83% and 80%. During the electrolysis process, the generated gas migrates vertically and horizontally under the influence of buoyancy and gas pressure. In the end of electrolysis, the gas inside the sand foundation basically migrates vertically only. The higher current intensity employed for electrolysis will affect the uniformity and stability of the gas. At constant currents of 1 A, 2 A and 3 A, the difference between the maximum and minimum degree of saturation in the treated foundation was 14%, 18% and 19%; and after electrolysis halted for 144 h, the saturation in the treated foundation was 90%, 85% and 87%. The electricity consumption analysis indicates that the desaturation method has excellent economic benefits in the treatment of saturated sand foundations.

scholarly journals Semi-Degree Threshold for Anti-Directed Hamiltonian Cycles

10.37236/3610 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Louis DeBiasio ◽  
Theodore Molla
Keyword(s):  
Directed Graph ◽  
Hamiltonian Cycle ◽  
Minimum Degree ◽  
Directed Graphs ◽  
Hamiltonian Cycles ◽  
Alternate Direction ◽  
Degree Conditions

In 1960 Ghouila-Houri extended Dirac's theorem to directed graphs by proving that if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $n/2$, then $D$ contains a directed Hamiltonian cycle. For directed graphs one may ask for other orientations of a Hamiltonian cycle and in 1980 Grant initiated the problem of determining minimum degree conditions for a directed graph $D$ to contain an anti-directed Hamiltonian cycle (an orientation in which consecutive edges alternate direction). We prove that for sufficiently large even $n$, if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $\frac{n}{2}+1$, then $D$ contains an anti-directed Hamiltonian cycle. In fact, we prove the stronger result that $\frac{n}{2}$ is sufficient unless $D$ is one of two counterexamples. This result is sharp.

NOTE ON MINIMUM DEGREE AND PROPER CONNECTION NUMBER

2020 ◽  
pp. 1-5
Author(s):  
YUEYU WU ◽  
YUNQING ZHANG ◽  
YAOJUN CHEN
Keyword(s):  
Minimum Degree ◽  
Connection Number ◽  
Minimum Value ◽  
Proper Connection Number ◽  
Degree Conditions

An edge-coloured graph $G$ is called properly connected if any two vertices are connected by a properly coloured path. The proper connection number, $pc(G)$ , of a graph $G$ , is the smallest number of colours that are needed to colour $G$ such that it is properly connected. Let $\unicode[STIX]{x1D6FF}(n)$ denote the minimum value such that $pc(G)=2$ for any 2-connected incomplete graph $G$ of order $n$ with minimum degree at least $\unicode[STIX]{x1D6FF}(n)$ . Brause et al. [‘Minimum degree conditions for the proper connection number of graphs’, Graphs Combin.33 (2017), 833–843] showed that $\unicode[STIX]{x1D6FF}(n)>n/42$ . In this note, we show that $\unicode[STIX]{x1D6FF}(n)>n/36$ .

Degree Kirchhoff Index of Bicyclic Graphs

2017 ◽  
Vol 60 (1) ◽  
pp. 197-205 ◽  
Author(s):  
Zikai Tang ◽  
Hanyuan Deng
Keyword(s):  
Connected Graph ◽  
Minimum Degree ◽  
Kirchhoff Index ◽  
Resistance Distance ◽  
Degree Of Vertex ◽  
Vertex Set ◽  
Maximum And Minimum Degree ◽  
Bicyclic Graphs

AbstractLet G be a connected graph with vertex set V(G).The degree Kirchhoò index of G is defined as S'(G) = Σ{u,v}⊆V(G) d(u)d(v)R(u, v), where d(u) is the degree of vertex u, and R(u, v) denotes the resistance distance between vertices u and v. In this paper, we characterize the graphs having maximum and minimum degree Kirchhoò index among all n-vertex bicyclic graphs with exactly two cycles.

scholarly journals On the ratio of maximum and minimum degree in maximal intersecting families

2013 ◽  
Vol 313 (2) ◽  
pp. 207-211
Author(s):  
Zoltán Lóránt Nagy ◽  
Lale Özkahya ◽  
Balázs Patkós ◽  
Máté Vizer
Keyword(s):  
Minimum Degree ◽  
Intersecting Families ◽  
Maximum And Minimum Degree

Minimum degree conditions for large subgraphs

2009 ◽  
Vol 34 ◽  
pp. 75-79
Author(s):  
Peter Allen ◽  
Julia Böttcher ◽  
Jan Hladký ◽  
Oliver Cooley
Keyword(s):  
Minimum Degree ◽  
Degree Conditions

Minimum Degree Conditions for the Proper Connection Number of Graphs

2017 ◽  
Vol 33 (4) ◽  
pp. 833-843 ◽  
Author(s):  
Christoph Brause ◽  
Trung Duy Doan ◽  
Ingo Schiermeyer
Keyword(s):  
Minimum Degree ◽  
Connection Number ◽  
Proper Connection Number ◽  
Degree Conditions

Minimum Degree and Disjoint Cycles in Claw-Free Graphs

2012 ◽  
Vol 21 (1-2) ◽  
pp. 129-139 ◽  
Author(s):  
RALPH J. FAUDREE ◽  
RONALD J. GOULD ◽  
MICHAEL S. JACOBSON
Keyword(s):  
Minimum Degree ◽  
Induced Subgraph ◽  
Subgraph Isomorphic ◽  
Disjoint Cycles ◽  
Large Order ◽  
Degree Conditions

A graph is claw-free if it does not contain an induced subgraph isomorphic to K1,3. Cycles in claw-free graphs have been well studied. In this paper we extend results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions. In particular, we prove that if G is claw-free of sufficiently large order n = 3k with δ(G) ≥ n/2, then G contains k disjoint triangles.

Sign in / Sign up

Export Citation Format

Share Document