The Path Partition Conjecture is true in generalizations of tournaments
نویسندگان
چکیده
The Path Partition Conjecture for digraphs states that for every digraph D, and every choice of positive integers λ1, λ2 such that λ1 + λ2 equals the order of a longest directed path in D, there exists a partition of D in two subdigraphs D1,D2 such that the order of the longest path in Di is at most λi for i = 1, 2. We present sufficient conditions for a digraph to satisfy the Path Partition Conjecture. Using this results, we prove that strong path mergeable, arc-locally semicomplete, strong 3quasi-transitive, strong arc-locally in-semicomplete and strong arc-locally out-semicomplete digraphs satisfy the Path Partition Conjecture. Some previous results are generalized.
منابع مشابه
Longest path partitions in generalizations of tournaments
We consider the so-called Path Partition Conjecture for digraphs which states that for every digraph, D, and every choice of positive integers, λ1, λ2, such that λ1 + λ2 equals the order of a longest directed path in D, there exists a partition of D into two digraphs, D1 and D2, such that the order of a longest path in Di is at most λi, for i = 1, 2. We prove that certain classes of digraphs, w...
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