# Search results for: Eckhard Steffen

Discussiones Mathematicae Graph Theory > 2017 > 38 > 1 > 165-175

Journal of Graph Theory > 87 > 2 > 135 - 148

Journal of Graph Theory > 85 > 2 > 363 - 371

Journal of Graph Theory > 84 > 2 > 109 - 120

*G*be a bridgeless cubic graph. Consider a list of

*k*1‐factors of

*G*. Let ${E}_{i}$ be the set of edges contained in precisely

*i*members of the

*k*1‐factors. Let ${\mu}_{k}\left(G\right)$ be the smallest $|{E}_{0}|$ over all lists of

*k*1‐factors of

*G*. We study lists by three 1‐factors, and call $G[{E}_{0}\cup {E}_{2}\cup {E}_{3}]$ with $|{E}_{0}|={\mu}_{3}\left(G\right)$ a ${\mu}_{3}\left(G\right)$‐core of

*G*. If

*G*is not 3‐edge‐colorable, then ${\mu}_{3}\left(G\right)\ge 3$. In Steffen (J Graph Theory 78 (2015), 195–206)...

Discrete Mathematics > 2016 > 339 > 11 > 2660-2663

*W*and a set of defaults

*D*. A sentence is defined to be derivable from a given default theory if it belongs to an extension of the default theory. A central question is: Given a default theory Δ = (

*D, W*) and a sentence

*β*, is there an...

Discrete Applied Mathematics > 2016 > 200 > C > 200-202

European Journal of Combinatorics > 2016 > 52 > PA > 234-243

Electronic Notes in Discrete Mathematics > 2015 > 49 > C > 51-55

European Journal of Combinatorics > 2015 > 48 > Complete > 34-47

Discrete Mathematics > 2015 > 338 > 6 > 866-867

Journal of Graph Theory > 79 > 1 > 1 - 7

Journal of Graph Theory > 78 > 3 > 195 - 206

*G*be a bridgeless cubic graph. Consider a list of

*k*1‐factors of

*G*. Let ${E}_{i}$ be the set of edges contained in precisely

*i*members of the

*k*1‐factors. Let ${\mu}_{k}\left(G\right)$ be the smallest $|{E}_{0}|$ over all lists of

*k*1‐factors of

*G*. Any list of three 1‐factors induces a core of a cubic graph. We use results on the structure of cores to prove sufficient conditions for Berge‐covers and for the existence of three...

Combinatorica > 2015 > 35 > 5 > 633-640

*G*be a bridgeless cubic graph, and

*μ*

_{2}(

*G*) the minimum number

*k*such that two 1-factors of

*G*intersect in

*k*edges. A cyclically

*n*-edge-connected cubic graph

*G*has a nowhere-zero 5-flow if (1)

*n*≥6 and

*μ*

_{2}(

*G*)≤2 or (2) if

*n*≥5

*μ*

_{2}(

*G*)−3.

Journal of Graph Theory > 76 > 4 > 297 - 308

*d*‐regular graphs. If

*d*is even, then ${F}_{d}^{c}=\left\{2\right\}$. For $d=2k+1$$(k\ge 1)$ it is known [] that ${F}_{2k+1}^{c}\cap (2+\frac{1}{k},2+\frac{2}{2k-1})=\varnothing $. We show that ${F}_{2k+1}^{c}=({F}^{c}-[2,2+\frac{2}{2k-1}))\cup \{2+\frac{1}{k}\}$. Hence, the interval $(2+\frac{1}{k},2+\frac{2}{2k-1})$ is the only gap for circular...

Discrete Mathematics > 2012 > 312 > 18 > 2757-2759

Journal of Graph Theory > 70 > 4 > 473 - 482

*G*is class II, if its chromatic index is at least Δ + 1. Let

*H*be a maximum Δ‐edge‐colorable subgraph of

*G*. The paper proves best possible lower bounds for |

*E*(

*H*)|/|

*E*(

*G*)|, and structural properties of maximum Δ‐edge‐colorable subgraphs. It is shown that every set of vertex‐disjoint cycles of a class II graph with Δ≥3 can be extended to a maximum Δ‐edge‐colorable subgraph. Simple graphs have...

Discrete Mathematics > 2012 > 312 > 2 > 476-478

Discrete Mathematics > 2010 > 310 > 3 > 385-389

Electronic Notes in Discrete Mathematics > 2007 > 28 > Complete > 239-242