Download Graph-Theoretic Concepts in Computer Science: 41st by Ernst W. Mayr PDF

By Ernst W. Mayr

This publication constitutes revised chosen papers from the 41st foreign Workshop on Graph-Theoretic thoughts in machine technology, WG 2015, held in Garching, Germany, in June 2015.
The 32 papers awarded during this quantity have been conscientiously reviewed and chosen from seventy nine submissions. They have been geared up in topical sections named: invited talks; computational complexity; layout and research; computational geometry; structural graph concept; graph drawing; and glued parameter tractability.

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Extra info for Graph-Theoretic Concepts in Computer Science: 41st International Workshop, WG 2015, Garching, Germany, June 17-19, 2015, Revised Papers

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Um } and {v1 , . . , vm } minus a perfect matching {u1 v1 , u2 v2 . . , um vm }. If the ordering is u1 , v1 , u2 , v2 , . . , um , vm , then First-Fit assigns colors 1, 1, 2, 2, . . , m, m, so m colors in total. However, assigning colors 1, 1, 2, 3 to the first four vertices u1 , v1 , u2 , v2 in this ordering requires only three colors in total. The algorithm for P7 -free bipartite graphs expands on this approach and uses two disjoint lists of colors for the bipartition classes of each connected component in the subgraph revealed so far.

Open Problem 1. Determine the complexity of Coloring for even-cycle-free graphs and even-anticycle-free graphs. Table 1. The complexity of k-Precoloring Extension and List k-Coloring on Pt -free bipartite graphs for fixed k and t. r k-Precoloring Ext. List k-Coloring k=3 k=4 k=5 k≥6 k=3 k=4 k=5 k≥6 t≤6 P P P P P P P P t=7 ? ? ? ? t=8 ? ? ? NP-c NP-c NP-c t=9 ? ? ? NP-c NP-c NP-c NP-c NP-c NP-c ? NP-c NP-c NP-c t ≥ 10 ? Bipartite and Chordal Bipartite Graphs. A graph is chordal bipartite if it is bipartite and every induced cycle has exactly four vertices.

Cycle-free Graphs. A hole is a cycle of on at least four vertices. An antihole is the complement of a hole. A cycle, hole or antihole is even if it contains an even number of vertices; otherwise it is odd. An (anti)hole is long if it has at least five vertices. A graph is odd-hole-free or odd-antihole-free if it contains no induced odd holes or no induced odd antiholes, respectively. In a similar way we define (even-)hole-free, (even-)antihole-free, long-hole-free, long-antihole-free, odd-cycle-free and (odd-)anticycle-free graphs.

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