scholarly journals A Note on Circuit Graphs

10.37236/459 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Qing Cui
Keyword(s):  
Short Proof ◽  
Closed Walk ◽  
Circuit Graph ◽  
Circuit Graphs

We give a short proof of Gao and Richter's theorem that every circuit graph contains a closed walk visiting each vertex once or twice.

The connectivity and Hamiltonian properties of second-order circuit graphs of wheel cycle matroids

2021 ◽  
Author(s):  
Zijian Deng ◽  
Bin Liu ◽  
Bofeng Huo ◽  
Bo Deng
Keyword(s):  
Minimum Degree ◽  
Second Order ◽  
First Order ◽  
Connected Matroid ◽  
Cycle Matroid ◽  
Hamiltonian Properties ◽  
Circuit Graph Of Matroid ◽  
Circuit Graph ◽  
Circuit Graphs

Let [Formula: see text] be the [Formula: see text]th-order circuit graph of a simple connected matroid M. The first-order circuit graph is also called a circuit graph. There are lots of results about connectivity and Hamiltonian properties of circuit graph of matroid, while there are few related results on the second-order circuit graph of a matroid. This paper mainly focuses on the connectivity and Hamiltonian properties of the second-order circuit graphs of the cycle matroid of wheels. It determines the minimum degree and connectivity of these graphs, and proves that the second-order circuit graph of the cycle matroid of a wheel is uniformly Hamiltonian.

A note on generalized quasi-contraction

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3091-3093
Author(s):  
Dejan Ilic ◽  
Darko Kocev
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Short Proof

In this paper we give a short proof of the main results of Kumam, Dung and Sitthithakerngkiet (P. Kumam, N.V. Dung, K. Sitthithakerngkiet, A Generalization of Ciric Fixed Point Theorems, FILOMAT 29:7 (2015), 1549-1556).

Short proof that Kneser graphs are Hamiltonian for n ⩾ 4k

2021 ◽  
Vol 344 (7) ◽  
pp. 112430
Author(s):  
Johann Bellmann ◽  
Bjarne Schülke
Keyword(s):  
Short Proof ◽  
Kneser Graphs

scholarly journals Strongly perfect claw‐free graphs—A short proof

2021 ◽  
Author(s):  
Maria Chudnovsky ◽  
Cemil Dibek
Keyword(s):  
Short Proof

scholarly journals A short note on extreme points of certain polytopes

2020 ◽  
Vol 8 (1) ◽  
pp. 36-39
Author(s):  
Lei Cao ◽  
Ariana Hall ◽  
Selcuk Koyuncu
Keyword(s):  
Short Proof ◽  
Convex Polytopes ◽  
Short Note ◽  
Convex Polytope ◽  
Extreme Points ◽  
Alternative Proof ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

scholarly journals A short proof of Gamas’s theorem

2009 ◽  
Vol 430 (2-3) ◽  
pp. 791-794 ◽  
Author(s):  
Andrew Berget
Keyword(s):  
Short Proof
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