Critical graph中文
http://www.ichacha.net/colour-critical%20graph.html Weba-factor-critical, 1-factor-critical, 2-factor-critical are respectively graphs with a perfect matching, factor-critical graphs as defined in [6], bicritical graphs as defined in [7]. For k and thus n even, a k-factor-critical graph is clearly ~-extendable. A k-factor-critical (q-extendable resp.) graph G is called minimal if for every edge
Critical graph中文
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WebA critical graph is a graph in which every vertex or edge is a critical element. A k-critical graph is a critical graph with chromatic number k; a graph G with chromatic number k … A $${\displaystyle k}$$-critical graph is a critical graph with chromatic number $${\displaystyle k}$$. A graph $${\displaystyle G}$$ with chromatic number $${\displaystyle k}$$ is $${\displaystyle k}$$-vertex-critical if each of its vertices is a critical element. Critical graphs are the minimal members in … See more In graph theory, a critical graph is an undirected graph all of whose subgraphs have smaller chromatic number. In such a graph, every vertex or edge is a critical element, in the sense that its deletion would decrease the … See more • Factor-critical graph See more • Jensen, T. R.; Toft, B. (1995), Graph coloring problems, New York: Wiley-Interscience, ISBN 0-471-02865-7 • Stiebitz, Michael; Tuza, Zsolt; See more
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Web5-critical graphs, that are stronger than the existing bounds. Keywords: Class one, class two, edge colouring, edge chromatic critical graphs AMS Mathematics Subject Classification (2010): 94C15 1. Introduction An edge-colouring of a graph is an assignment of colours to its edges so that no two adjacent edges are assigned the same colour. WebDec 20, 2024 · This graph is k 1 + k 2 critical. So pick some large n, pick two graphs on n / 2 vertices which are both k / 2 -critical and join them as above. This shows that the minimum degree is not only unbounded, but it can grow linearly in the number of vertices!
WebDec 12, 2024 · $\begingroup$ Also, it's interesting to observe that critical and not complete graphs can be uniquely colorable under a more flexible definition: one that includes graph automorphisms. For example, the $5$-cycle is $3$-critical. All colorings of it "look the same" in that we can start at a vertex and go around the cycle to see an A-B-A-B-C pattern.
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