In human-centered assembly systems, workers adapt to new and changing tasks based on learning processes. Human factors are crucial for the entire system capability in such kind of systems. Current methodologies scheduling often take only limited account human interaction between workforce planning. Although extensive research indicates that a careful introduction implies many benefits, examples reduction errors, increasing flexibility performance as well wellbeing. The developed methodology...

Abstract An r -regular graph is an -graph, if every odd set of vertices connected to its complement by at least edges. Let G and H be -graphs. -coloring a mapping $$f:E(G) \rightarrow E(H)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> <mml:mo>→</mml:mo> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> such that each adjacent edges are mapped . For $$r\ge 3$$...

Abstract Let G be a bridgeless cubic graph. Consider list of k 1‐factors . the set edges contained in precisely i members 1‐factors. smallest over all lists Any three induces core We use results on structure cores to prove sufficient conditions for Berge‐covers and existence with empty intersection. Furthermore, if , then is an upper bound girth also some new bounds length shortest cycle covers graphs. Cubic graphs have 4‐cycle cover 5‐cycle double cover. These satisfy two conjectures Zhang...

Abstract Let ( be two positive integers. We generalize the well‐studied notions of ‐colorings and circular chromatic number to signed graphs. This implies a new notion colorings graphs, corresponding χ. Some basic facts on graphs are proved, differences results unsigned analyzed. In particular, we show that difference between graph is at most 1. Indeed, there where On other hand, for n vertices, if smaller than 1, then exists , such . also equivalent r (see [12] (X. Zhu, Recent developments...

There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the $5$-cycle double cover which would be true general if they for cubic graphs. Since most of them trivially $3$-edge-colorable graphs, graphs not $3$-edge-colorable, often called snarks, play a key role this context. Here, we survey parameters measuring how far apart non is from being $3$-edge-colorable. We study their interrelation prove some new results. Besides getting insight into structure show that...

In this paper we study Petersen-colorings and strong on some well known families of snarks, e.g. Blanuša Goldberg snarks flower snarks. particular, it is shown that have a Petersen-coloring but they do not Petersen-coloring. Furthermore proved possible minimum counterexamples to Jaeger's conjecture contain specific subdivision K 3, 3 .

Abstract Let G be a bridgeless cubic graph. Consider list of k 1‐factors . the set edges contained in precisely i members 1‐factors. smallest over all lists We study by three 1‐factors, and call with ‐core If is not 3‐edge‐colorable, then In Steffen (J Graph Theory 78 (2015), 195–206) it shown that if , an upper bound for girth show bounds oddness as well. prove every has very specific structure. these cores Petersen cores. any given there cyclically 4‐edge‐connected graph On other hand,...

.Thomassen [J. Combin. Theory Ser. B, 141 (2020), pp. 343–351] asked whether every \(r\) -edge-connected -regular graph of even order has \(r-2\) pairwise disjoint perfect matchings. We show that this is not the case if \(r \equiv 2 \text{ mod } 4\) . Together with a recent result Mattiolo and Steffen Graph Theory, 99 (2022), 107–116] solves Thomassen's problem for all It turns out our methods are limited to problem. then prove some equivalences statements on matchings in highly...

The circular flow number Fc(G) of a graph G = (V, E) is the minimum r ϵ ℚ such that admits ϕ with 1 ≤ (e) − 1, for each e E. We determine some regular multigraphs. In particular, we characterize bipartite (2t+1)-regular graphs (t ≥ 1). Our results imply there are gaps possible numbers graphs, e.g., no cubic 3 < 4. further show snarks arbitrarily close to 4, answering question X. Zhu. © 2000 John Wiley & Sons, Inc. J Graph Theory 36: 24–34, 2001

Abstract A graph G is class II, if its chromatic index at least Δ + 1. Let H be a maximum Δ‐edge‐colorable subgraph of . The paper proves best possible lower bounds for | E ( )|/| )|, and structural properties subgraphs. It shown that every set vertex‐disjoint cycles II with Δ≥3 can extended to subgraph. Simple graphs have such the complement matching. Furthermore, simple always I. © 2011 Wiley Periodicals, Inc. J Graph Theory

Abstract In 1968, Vizing made the following two conjectures for graphs which are critical with respect to chromatic index: (1) every graph has a 2‐factor, and (2) independent vertex set in contains at most half of vertices. We prove both many edges, determine upper bounds size sets those graphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 113–118, 2004