A short proof that every finite graph has a tree-decomposition displaying its tangles

We give short proofs of the following two results: Thomas's theorem that every finite graph has a linked tree-decomposition of width no greater than its tree-width; and the ‘tree-width duality theorem’ of Seymour and Thomas, that the tree-width of a finite graph is exactly one less than the largest order of its brambles.

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A note on generalized quasi-contraction

Filomat ◽

10.2298/fil1711091i ◽

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).

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

Discrete Mathematics ◽

10.1016/j.disc.2021.112430 ◽

2021 ◽

Vol 344 (7) ◽

pp. 112430

Author(s):

Johann Bellmann ◽

Bjarne Schülke

Keyword(s):

Short Proof ◽

Kneser Graphs

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Strongly perfect claw‐free graphs—A short proof

Journal of Graph Theory ◽

10.1002/jgt.22659 ◽

2021 ◽

Author(s):

Maria Chudnovsky ◽

Cemil Dibek

Keyword(s):

Short Proof

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A short note on extreme points of certain polytopes

Special Matrices ◽

10.1515/spma-2020-0005 ◽

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.

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