scholarly journals An application of Vizing and Vizing-like adjacency lemmas to Vizing’s Independence Number Conjecture of edge chromatic critical graphs

2009 ◽  
Vol 309 (9) ◽  
pp. 2925-2929 ◽  
Author(s):  
Rong Luo ◽  
Yue Zhao
Keyword(s):  
Independence Number ◽  
Critical Graphs

Independence number and minimum degree for fractional ID-k-factor-critical graphs

2012 ◽  
Vol 84 (1-2) ◽  
pp. 71-76 ◽  
Author(s):  
Sizhong Zhou ◽  
Lan Xu ◽  
Zhiren Sun
Keyword(s):  
Minimum Degree ◽  
Independence Number ◽  
Critical Graphs ◽  
K Factor

Bounds for the Independence Number of Critical Graphs

2000 ◽  
Vol 32 (2) ◽  
pp. 137-140 ◽  
Author(s):  
Gunnar Brinkmann ◽  
Sheshayya A. Choudum ◽  
Stefan Grünewald ◽  
Eckhard Steffen
Keyword(s):  
Independence Number ◽  
Critical Graphs

scholarly journals On the independence number of edge chromatic critical graphs

2014 ◽  
Vol 34 (3) ◽  
pp. 577 ◽  
Author(s):  
Lianying Miao ◽  
Zhengke Miao ◽  
Shiyou Pang ◽  
Wenyao Song
Keyword(s):  
Independence Number ◽  
Critical Graphs

Valued Field Graph and Some Related Parameters

2020 ◽  
pp. 389-395
Author(s):  
G. Suresh Singh ◽  
P. K. Prasobha
Keyword(s):  
Finite Field ◽  
Independence Number ◽  
Valued Field ◽  
Vertex Set ◽  
Adic Valuation

Let $K$ be any finite field. For any prime $p$, the $p$-adic valuation map is given by $\psi_{p}:K/\{0\} \to \R^+\bigcup\{0\}$ is given by $\psi_{p}(r) = n$ where $r = p^n \frac{a}{b}$, where $p,a,b$ are relatively prime. The field $K$ together with a valuation is called valued field. Also, any field $K$ has the trivial valuation determined by $\psi{(K)} = \{0,1\}$. Through out the paper K represents $\Z_q$. In this paper, we construct the graph corresponding to the valuation map called the valued field graph, denoted by $VFG_{p}(\Z_{q})$ whose vertex set is $\{v_0,v_1,v_2,\ldots, v_{q-1}\}$ where two vertices $v_i$ and $v_j$ are adjacent if $\psi_{p}(i) = j$ or $\psi_{p}(j) = i$. Here, we tried to characterize the valued field graph in $\Z_q$. Also we analyse various graph theoretical parameters such as diameter, independence number etc.

scholarly journals Improvement on the Crossing Number of Crossing-Critical Graphs

2020 ◽  
Author(s):  
János Barát ◽  
Géza Tóth
Keyword(s):  
Crossing Number ◽  
Critical Graphs ◽  
Minimum Number ◽  
Edge Crossings

AbstractThe crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. A graph G is k-crossing-critical if its crossing number is at least k, but if we remove any edge of G, its crossing number drops below k. There are examples of k-crossing-critical graphs that do not have drawings with exactly k crossings. Richter and Thomassen proved in 1993 that if G is k-crossing-critical, then its crossing number is at most $$2.5\, k+16$$ 2.5 k + 16 . We improve this bound to $$2k+8\sqrt{k}+47$$ 2 k + 8 k + 47 .

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